Blejske delavnice iz fizike Letnik 20, št. 1 Bled Workshops in Physics Vol. 20, No. 1 ISSN 1580-4992 Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Edited by Bojan Golli Mitja Rosina Simon Sirca University of Ljubljana and Jozef Stefan Institute dmfa - ZALOŽNIŠTVO Ljubljana, november 2019 The Mini-Workshop Electroweak Processes ofHadrons was organized by Society of Mathematicians, Physicists and Astronomers of Slovenia Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana and sponsored by Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana Jožef Stefan Institute, Ljubljana Society of Mathematicians, Physicists and Astronomers of Slovenia Partially Supported by University of Graz Organizing Committee Mitja Rosina, Bojan Golli, Simon Sirca List of participants Roelof Bijker, Ciudad de México, bijker@nucleares.unam.mx Marko Bračko, Ljubljana, marko.bracko@ijs.si Gernot Eichmann, Lisbon, gernot.eichmann@tecnico.ulisboa.pt Harald Fritzsch, Munich, fritzch@mpp.mpg.de Bojan Golli, Ljubljana, bojan.golli@ijs.si Marek Karliner, Tel Aviv, marek@tauex.tau.ac.il Hyun-Chul Kim, Incheon, South Korea, hchkim@inha.ac.kr June-Young Kim, Incheon, South Korea, juneyoung.ghim@gmail.com Raquel Molina Peralta, Madrid, raqumoli@ucm.es Willi Plessas, Graz, willibald.plessas@uni-graz.at Saša Prelovšek, Ljubljana, sasa.prelovsek@ijs.si Mitja Rosina, Ljubljana, mitja.rosina@ijs.si Jonathan Rosner, Chicago, rosner@hep.uchicago.edu Helios Sanchis Alepuz, Graz, helios.sanchis-alepuz@uni-graz.at Jugoslav Stahov, Tuzla, jugoslav.stahov@untz.ba Finn Stokes, Jülich, f.stokes@fz-juelich.de Simon Sirca, Ljubljana, simon.sirca@fmf.uni-lj.si Herbert Weigel, Stellenbosch, South Africa, weigel@sun.ac.za Electronic edition (in colour) http://www-f1.ijs.si/BledPub/ The presentations can be found at http://www-f1.ijs.si/Bled2019/Program.html The articles are peer reviewed by the Editorial Board Contents Preface............................................................. V Predgovor..........................................................VII Photocouplings of pentaquark states Roelof Bijker and Emmanuel Ortiz-Pacheco............................. 1 Resonances and contour deformations Gernot Eichmann.................................................... 5 Flavor Mixing, Neutrino Oscillations and Neutrino Masses Harald Fritzsch...................................................... 9 Hidden Charm Molecular Pentaquarks: Some Open Questions Marek Karliner...................................................... 15 A unified approach for the structure of light and heavy baryons Hyun-Chul Kim..................................................... 21 Improved pion mean fields June-Young Kim, Hyun-Chul Kim..................................... 25 Light- and strange-quark mass dependence of the p (770) meson properties R. Molina, J. Ruiz de Elvira............................................ 29 Electromagnetic Form Factors of the Nucleons, the A, and the Hyperons W.Plessas.......................................................... 43 Heavy-Quark Exotics Jonathan L. Rosner................................................... 48 Effect of intermediate resonances in the quark-photon vertex Helios Sanchis-Alepuz ............................................... 57 IV Contents Partial Wave Analysis of Pion Photoproduction Data with Fixed-t Ana-lyticity Imposed J. Stahov, H. Osmanovic, M. HadZimehmedovic, R. Omerovic............. 63 Structure and transitions of nucleon excitations from lattice QCD Finn M. Stokes, Waseem Kamleh, Derek B. Leinweber.................... 68 Exotic Baryons in Skyrme Type Models H. Weigel........................................................... 75 News from Belle on Hadron Spectroscopy M. Bracko........................................................... 80 The enigmatic A(1600) resonance B.Golli............................................................. 85 A phenomenological lower bound for the E++ mass MitjaRosina ........................................................ 89 Measurement of GA and the GDH sum rule at high energies at Jefferson Lab: two proposals S. Sirca............................................................. 93 Povzetki v slovenscini...............................................103 Preface At the beautiful Lake Bled, the tradition of hadronic Mini-Workshops with their lively discussions continues. We are happy to greet our regular participants, as well as to attract new devotees. At every new meeting we witness upgrades of previously discussed topics and seed new ones. Electroweak form-factors are a perennial repertory on our stage, and we have heard of new proposals to accurately measure the nucleon electromagnetic and axial form factors. The covariant relativistic approach in the constituent quark model that was so successful for the nucleons has been extended A, A I and n baryons. Its success is based on including the essential degrees of freedom and respecting the relevant symmetries. Good fits are typically achieved without resorting to five-quark admixtures, and there seems to be no evidence for diquark clustering. The ideas of the chiral quark-soliton model with mesonic mean fields have also been extended to calculate the spectra and the structure of heavy baryons. Strong mixing effects are expected in the case of light baryons belonging to different SU(3) flavour representations. Both static and dynamic electromagnetic properties test our models and understanding of new phenomena. Electro- and photo-excitation has always been a favourite topic at Bled, and it was no different this time around: through these processes one explores not only the photoproduction of pions and light baryon resonances, but also exotic hadrons such as pentaquarks. The advances in analytic methods for resonances have clarified some open questions about nucleon resonances, such as the Roper N(1440) and A(1600). This year's "champions" were the recently discovered double-heavy baryons. They pave the way to potentially rich spectra and to double-heavy exotics. We discussed phenomenological methods for the calculation of double-heavy baryons, tetraquarks and "molecules" such as dimesons DO, DD* and pentaquarks. There is evidence that the heavy quarks stabilize such molecules. Lattice QCD simulations, apart from being a bleeding-edge approach by itself, continue to be a most welcome supplement to quark model calculations. The examples discussed at the Workshop were the Zb tetraquarks, the p meson decay parameters, and the parity expanding technique for extractions of the elastic and transition form factors involving the nucleon ground state and its excitations. Quark and lepton flavour mixing angles and neutrino masses, are always a "hit" suitable to animate a meeting. It is interesting to see how the assumption of four vanishing matrix elements in the mass matrix can give realistic relations between masses and mixing angles. Ljubljana, November 2019 B. Golli, M. Rosina, S. Sirca Predgovor Ob prelepem Blejskem jezeru se nadaljuje tradicija hadronskih Mini-delavnic z značilnimi Živahnimi diskusijami. Z veseljem pozdravljamo stalne udeleZence in pritegujemo nove navdusence. Na vsakem novem srečanju smo priča nadgradnji prejšnjih tem in sejemo semena novih. Elektrosibki oblikovni faktorji na nasem odru sodijo ze v dolgoletni repertoar, letos pa smo slisali tudi nove predloge, kako natancneje meriti elektromagnetne in aksialne oblikovne faktorje nukleona. Kovariantni relativisticni pristop pri modelu s konstituentnimi kvarki, ki se je tako dobro izkazal za nukleon, so razsirili se na barione A, A, I in H. Uspeh pristopa sloni na upostevanju bistvenih pros-tostnih stopenjin spostovanju pomembnih simetrij. Dobro ujemanje so znacilno dosegli brez petkvarkovskih primesi; zdi se tudi, da ni evidence za dvokvarkovske gruce v omenjenih barionih. Zamisli kiralnega solitonskega modela s kvarki v povprecnem mezonskem polju so razsirili tudi na racune spektrov in zgradbe tezkih barionov. Pricakujejo pa se znatni ucinki mesanja pri lahkih barionih, ki pripadajo razlicnim upodobitvam grupe SU(3) za okuse. Tako staticne kot dinamicne elektromagnetne lastnosti preverjajo nase modele in razumevanje novih pojavov. Elektronsko in fotonsko vzbujanje sta bila vedno priljubljena tema na Bledu in tudi to pot ni bilo nic drugace: s temi procesi ne raziskujemo zgoljfotoprodukcije pionov in lahkih barionskih resonanc, temvec tudi eksoticne hadrone, na primer pentakvarke. Napredek pri analiticnih metodah za resonance pa je pojasnil nekatera odprta vprasanja o nukleonskih resonancah, kot so Roperjeva, N(1440), in A(1600). Letosnji "junaki" so bili nedavno odkriti dvojno tezki barioni. Utirajo pot morda bogatim spektrom in dvojno tezkim eksoticnim hadronom. Razpravljali smo o fenomenoloskih metodah za racunanje dvojno tezkih barionov, tetrakvarkov in "molekul", kot so dimezoni DD, DD* in pentakvarki. Izkusnje podpirajo zamisel, da tezki kvarki stabilizirajo taksne molekule. Simulacije s kromodinamiko na mrezi, ki so avantgarda same po sebi, so do-brodoslo dopolnilo tudi za racune s kvarkovimi modeli. Razpravljali smo o zgledih, kot so tetrakvark Zb, razpadni parametri mezona p in metoda za razvoj po parnostih za elasticne in prehodne oblikovne faktorje osnovnega in vzbujenih stanj nukleona. Mesalni koti za okuse pri kvarkih in leptonih ter mase nevtrinov so "pozivilo" prenekaterega srecanja. Zanimivo je bilo videti, kako predpostavka o stirih nicel-nih matricnih elementih v masni matriki vodi do realisticnih povezav med masami in mesalnimi koti. Ljubljana, november 2019 B. Golli, M. Rosina, S. Sirca Workshops organized at Bled > What Comes beyond the Standard Model (June 29-July 9, 1998), Vol. 0 (1999) No. 1 (July 22-31,1999) (July 17-31, 2000) (July 16-28, 2001), Vol. 2 (2001) No. 2 (July 14-25, 2002), Vol. 3 (2002) No. 4 (July 18-28,2003), Vol. 4 (2003) Nos. 2-3 (July 19-31, 2004), Vol. 5 (2004) No. 2 (July 19-29, 2005), Vol. 6 (2005) No. 2 (September 16-26, 2006), Vol. 7 (2006) No. 2 (July 17-27, 2007), Vol. 8 (2007) No. 2 July 15-25, 2008), Vol. 9 (2008) No. 2 July 14-24, 2009), Vol. 10 (2009) No. 2 July 12-22, 2010), Vol. 11 (2010) No. 2 July 11-21, 2011), Vol. 12 (2011) No. 2 July 9-19, 2012), Vol. 13 (2012) No. 2 July 14-21, 2013), Vol. 14 (2013) No. 2 July 20-28, 2014), Vol. 15 (2014) No. 2 July 11-20, 2015), Vol. 16 (2015) No. 2 July 11-19, 2016), Vol. 17 (2016) No. 2 July 10-18, 2017), Vol. 18 (2017) No. 2 June 23-30, 2018), Vol. 19 (2018) No. 2 July 6-14, 2019), Vol. 20 (2019) No. 2 > Hadrons as Solitons (July 6-17,1999) > Few-Quark Problems (July 8-15, 2000), Vol. 1 (2000) No. 1 > Statistical Mechanics of Complex Systems (August 27-September 2, 2000) > Selected Few-Body Problems in Hadronic and Atomic Physics (July 7-14,2001), Vol. 2 (2001) No. 1 > Studies of Elementary Steps of Radical Reactions in Atmospheric Chemistry (August 25-28, 2001) > Quarks and Hadrons (July 6-13, 2002), Vol. 3 (2002) No. 3 > Effective Quark-Quark Interaction (July 7-14, 2003), Vol. 4 (2003) No. 1 > Quark Dynamics (July 12-19, 2004), Vol. 5 (2004) No. 1 > Exciting Hadrons (July 11-18, 2005), Vol. 6 (2005) No. 1 > Progress in Quark Models (July 10-17, 2006), Vol. 7 (2006) No. 1 > Hadron Structure and Lattice QCD (July 9-16, 2007), Vol. 8 (2007) No. 1 > Few-Quark States and the Continuum (September 15-22, 2008), Vol. 9 (2008) No. 1 > Problems in Multi-Quark States (June 29-July 6, 2009), Vol. 10 (2009) No. 1 > Dressing Hadrons (July 4-11, 2010), Vol. 11 (2010) No. 1 > Understanding hadronic spectra (July 3-10, 2011), Vol. 12 (2011) No. 1 > Hadronic Resonances (July 1-8, 2012), Vol. 13 (2012) No. 1 > Looking into Hadrons (July 7-14, 2013), Vol. 14 (2013) No. 1 > Quark Masses and Hadron Spectra (July 6-13, 2014), Vol. 15 (2014) No. 1 > Exploring Hadron Resonances (July 5-11, 2015), Vol. 16 (2015) No. 1 > Quarks, Hadrons, Matter (July 3-10, 2016), Vol. 17 (2016) No. 1 > Advances in Hadronic Resonances (July 2-9, 2017), Vol. 18 (2017) No. 1 > Double-charm baryons and dimesons (June 17-23, 2018), Vol. 19 (2018) No. 1 > Electroweak Processes of Hadrons (July 15-19, 2019), Vol. 20 (2019) No. 1 Bled Workshops in Physics Vol. 20, No. 1 p.l A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Photocouplings of pentaquark states* Roelof Bijker and Emmanuel Ortiz-Pacheco Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Ciudad de Mexico, Mexico Abstract. In this contribution, we discuss the electromagnetic couplings of pentaquark states with hidden charm. This work is motivated by recent experiments at CERN by the LHCb Collaboraton and current experiments at JLab to confirm the existence of hidden-charm pentaquarks in photoproduction experiments. 1 Introduction The observation of possible hidden-charm pentaquark states by the LHCb Collaboration [1,2] has led to an enormous amount of theoretical studies on the nature of these states and on different possible interpretations of the observed signals, e.g. kinematical effects, molecular states, compact pentaquarks, mesonbaryon states coupled to a five-quark compact core [3]-[8] and baryo-quarkonium states [9]. In addition, new experiments were suggested at JLab to confirm the existence of hidden-charm pentaquarks in photoproduction experiments [10]-[15]. In the present contribution we discuss the electromagnetic couplings of uudcc hidden-charm pentaquark states which are relevant for the photoproduction experiments at JLab. 2 Pentaquark states Pentaquark states depend both on the orbital degrees of freedom and the internal degrees of freedom of color, spin and flavor The construction of the classification scheme of uudcc pentaquark states was carried out explicitly in Ref. [16] using the following two conditions: (i) the pentaquark wave function should be a color singlet and (ii) the wave function of the four-quark subsystem should be antisymmetric. The permutation symmetry of four-quark states can be characterized by the S4 Young tableaux [4], [31], [22], [211] and [1111] or, equivalently, by the irreducible representations of the tetrahe-dral group Td (which is isomorphic to S4) as Ai, F2, E, Fi and A2, respectively. * Talk presented by Roelof Bijker (1) 2 Roelof Bijker and Emmanuel Ortiz-Pacheco The first condition that the pentaquark wave function has to be a color-singlet, implies that the color wave function of the four-quark configuration has to be a [211] triplet with F1 symmetry under Td. As a consequence, the second condition that the total q4 wave function has to be antisymmetric (A2), means that the orbital-spin-flavor part is a [31] triplet with F2 symmetry ^ x ^osf '2 A2 (2) where the subindices refer to the symmetry properties of the four-quark subsystem under permutation. In this contribution we discuss ground-state pentaquark states, i.e. without orbital excitations, which means that the orbital part of the pentaquark wave functions is symmetric (Ai). Therefore, the spin-flavor part is a [31] state with F2 symmetry ^ = ^A, x < A2 (3) In Ref. [16] it was shown that there are in total seven uudcc ground-state pentaquark configurations with angular momentum and parity JP = 3/2- (which is quoted in the literature as the most likely value of the angular momentum and parity of the Pc pentaquark [1]), three of which belong to a flavor decuplet and the remaining four to a flavor octet (see Fig. 1 and first column of Table 1). uudcc uudcc jN _ - PC/PA P A P c Z P c Pc U P c Fig. 1. Pentaquark decuplet and octet 3 Electromagnetic couplings For experiments that aim to study pentaquarks through near threshold J/^ photoproduction at JLab, the size of the electromagnetic couplings of the pentaquarks is important. Here we discuss the electromagnetic couplings for the ground state pentaquarks with spin and parity JP = 3/2-. For the process of interest, Pc —» N + y, the relevant contribution is the annihilation of a pair of cc quarks (see Fig. 2). In the present calculation we use the nonrelativistic form of the interaction. The radiative decay widths can be calculated as r(Pc -> N + y) = ^ J-y X |Av(k)|2 , (4) (2n)2 2J + 1 V>0 Photocouplings of pentaquark states 3 where p is the phase space factor, and Av denotes the helicity amplitude Av(k) = (N,1/2+ - 1;YlHmiPc,3/2-,v) = ^ — pv F(k) . (5) Here a is the fine-structure constant, and k0 and k = |k| represent the energy and the momentum of the photon. The coefficient pv is the contribution from the color-spin-flavor part for the annihilation of a cc color-singlet pair with spin S = Sz = 1. The color-spin-flavor part is common to all quark models. In Table 1 we show the results for the contribution from the color-spin-flavor part to the helicity amplitudes for different configurations of uudcc pentaquarks [16]. Out of a total of seven uuddc ground-state pentaquark configurations only three have nonvanishing photocouplings, all corresponding to octet pentaquarks. The strongest coupling is to the octet pentaquark configuration with , followed by ^e and . Fig. 2. Electromagnetic decay of pentaquark Pc into a baryon B and a photon, Pc —> B + y. Since the photon momentum for the photocouplings Pc —» N + y is large (of the order of k ~ 2.1 GeV), one expects a large suppression due to the form factor F(k) which denotes the contribution from the orbital part of the pentaquark wave function. Although its specific form depends on the type of quark model used: harmonic oscillator, hypercentral, or other, for this value of the photon momentum the effect is large resulting in a very small photocoupling. The first measurement of the J/^ exclusive photoproduction cross section by the GlueX Collaboration saw no evidence for the LHCb pentaquark candidates Pc [17]. 4 Summary and conclusions In conclusion, in this contribution we discussed the electromagnetic couplings of ground-state uudcc pentaquark states with angular momentum and parity JP = 3/2-. It was shown that only three pentaquark configurations, all belonging to a flavor octet, have a nonvanishing photocoupling. Since the photon momentum is large, we expect that these couplings are strongly suppressed by the form factor, F(k), representing the contribution from the orbital part of the pen-taquark wave function. This seems to be confirmed in recent photoproduction 4 Roelof Bijker and Emmanuel Ortiz-Pacheco Table 1. Contribution from the color-spin-flavor part to the helicity amplitudes for the electromagnetic decays of uudcc decuplet (top) and octet (bottom) pentaquark states into N + y [16]. Here ec is the electric charge of the charm quark ec = 2/3. State Name ß 1/2 ß3/2 [$A, X XF2 ]F2 pA r c 0 0 X XA, ]F2 pA pc 0 0 X XF2^ ]F2 pA pc 0 0 [^F2 X XA, ]F2 pN pc 0 0 [^F2 X XF2^ ]F2 pN pc 675 ec 276 e X XF2 ] F2 pN pc - 6 ec - 273e' X XF2^ ]F2 pN pc - 276 ec - 2772 e' c c c experiments by the GlueX Collaboration in which no evidence was found for the Pc pentaquarks. It is important to emphasize that this null result does not rule out an interpretation of the LHCb signals in terms of pentaquarks. Acknowledgements This work was supported in part by grant IN109017 from DGAPA-UNAM, Mexico and grants 251817 and 340629 from CONACyT, Mexico. References 1. Aaij R et al. (LHCb Collaboration) 2015 Phys. Rev. Lett. 115 072001 2. Aaij R et al. (LHCb Collaboration) 2019 Phys. Rev. Lett. in press [arXiv:1904.03947] 3. Chen H X, Chen W, Liu X and Zhu S L 2016 Phys. Rep. 639 1 4. Esposito A, Pilloni A and Polosa A D 2016 Phys. Rep. 668 1 5. Ali A, Lange J S and Stone S 2018 Prog. Part. Nucl. Phys. 97 123 6. Olsen S L, Skwarnicki T and Zieminska D 2018 Rev. Mod. Phys. 90 015003 7. Karliner M, Rosner J L and Skwarnicki T 2018 Ann. Rev. Nucl. Part. Sci. 68 17 8. Guo F-K, Hanhart C, Meißner U-G, Wang Q, Zhao Q and Zou B-S 2018 Rev. Mod. Phys. 90 015004 9. Ferretti J, Santopinto E, Naeem Anwar M and Bedolla M A 2019 Phys. Lett. B 789 562 10. Kubarovsky V and Voloshin M B 2015 Phys. Rev. D 92 031502(R) 11. Wang Q, Liu X H and Zhao Q 2015 Phys. Rev. D 92 034022 12. Karliner M and Rosner J L 2016 Phys. Lett. B 752 329 13. Hiller Blin A N, Fernandez-Ramirez C, Jackura A, Mathieu V, Mokeev V I, Pilloni A and Szczepaniak A P 2016 Phys. Rev. D 94 034002 14. Fernandez-Ramirez C, Hiller Blin A N and Pilloni A 2017 J Phys ConfSer 876 012007 15. Meziani Z E et al. 2016 arXiv:1609.00676 16. Ortiz-Pacheco E, Bijker R and Fernandez-Ramirez C 2019 J. Phys. G: Nucl. Part. Phys. 46 065104 [arXiv:1808.10512] 17. Ali A et al. (GlueX Collaboration) 2019 Phys Rev Lett 123 072001 Bled Workshops in Physics Vol. 20, No. 1 P. 5 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Resonances and contour deformations Gemot Eichmann CFTP, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal Abstract. We exemplify the extraction of resonance properties from Lorentz-invariant integral equations. To this end we solve the Bethe-Salpeter and scattering equations for a scalar model and determine the resonance pole locations and phase shifts. It turns out that the scalar model does not produce resonance poles in the complex plane but instead virtual states on the real axis of the second Riemann sheet. Understanding the properties of resonances is a central task in nonpertur-bative QCD studies. Most of the 'bound states' in QCD are actually resonances which decay and thus correspond to poles in the complex momentum plane of scattering amplitudes. In the following we focus on the extraction of resonances from Lorentz-invariant integral equations, which is motivated by calculations of hadron spectra and matrix elements in the functional approach of Dyson-Schwinger equations (DSEs) and Bethe-Salpeter equations (BSEs), see e.g. [1-3] and references therein. These calculations typically use a Euclidean metric, and even though a 'naive' Euclidean integration path allows one to calculate non-perturbative propagators, vertices and Bethe-Salpeter amplitudes in the complex momentum plane, one is typically limited by the nearest singularities appearing in the integrands. As a consequence, the calculations are restricted to low-lying meson and baryon excitations, states below thresholds, and form factors within a certain Q2 range. As discussed below, in principle these obstacles can be overcome by employing contour deformations [4-12]. Another motivation for our work is to build a bridge toward similar calculations using a Minkowski metric, see e.g. [13-17]. We exemplify the situation for a scalar theory consisting of two scalar fields with masses m and |i and a three-point interaction. This leaves two parameters, namely a dimensionless coupling constant c = g2/(4nm)2 and the mass ratio |3 = |/m. The relevant equations are shown in Fig. 1: The first is the homogeneous BSE, which determines the mass spectrum and BS amplitude in a given JPC channel; the second is the inhomogeneous BSE which determines the corresponding vertex function; and the third is the scattering equation which determines the scattering amplitude. For simplicity we work with tree-level propagators and restrict the kernel to a scalar ladder exchange with mass | , which is the massive Wick-Cutkosky model [18-20]. For details on the setup and solution techniques we refer to Ref. [12]; in particular, we use a Euclidean metric and do not employ further approximations such as three-dimensional reductions but instead solve the full Lorentz-invariant integral equations in four dimensions. 6 Gernot Eichmann Im Vt Im Vt" - 1 Bound states Re VF \A Fig. 1. Left: singularity structure in the complex Vt plane. Right: homogenous BSE, inho-mogeneous BSE and scattering equation. + The left panel in Fig. 1 shows the typical singularity structure in the complex plane of the variable %/t, where t = P2/(4m2) is the total momentum squared in Euclidean conventions (i.e., positive t means spacelike and negative t timelike). Below the threshold ImVt = 1 there can be bound states on the imaginary Vt axis, whose locations depend on the parameters c and p. The two-particle cut starts at the threshold and extends to infinity, and above the threshold one would expect resonances on the second Riemann sheet, with complex masses Mi corresponding to ImVt = ReMt/(2m). Let us investigate the trajectory of the ground-state pole depending on the coupling c. A stronger coupling entails stronger binding, so that by increasing c the pole will slide down on the imaginary axis. Below a certain coupling strength the pole (presumably) moves above the threshold and becomes a resonance, whereas above a certain strength it becomes tachyonic and continues its trajectory on the real %/t axis. In our context, the latter case is mainly a truncation artifact: since the internal propagators remain at tree level, they do not depend on c which can be tuned freely; hence there is always a critical strength above which the state becomes tachyonic. This is most clearly seen from the eigenvalues of the homogeneous BSE, cf. Fig. 10 in Ref. [12]. As a consequence, the ground state is bound only within a certain window of the parameter c. If one increases the coupling further, eventually the first excited state becomes bound and follows a similar trajectory, followed by the second excited state and so on. These properties readily follow from solving the homogeneous BSE for real values of t > — 1. The question is therefore: What is the nature of a state before it becomes bound, i.e., for small couplings? To answer it, one has to overcome several technical difficulties. Solving the BSE for complex values of %/t is only straightforward as long as ImVt < 1, which is the colored region in Fig. 1. To access the first sheet above the threshold, however, one must employ contour deformations: After integrating over the inner integration variable, the poles in the integrand from the constituent and exchange propagators become cuts and one has to deform the integration path in the outer integration variable to avoid those cuts. A contour deformation in the Euclidean metric is equivalent to picking up the correct poles in a Minkowski treatment, which is colloquially referred to as 'going to Minkowski space'. With contour Resonances and contour deformations 7 2nd sheet 1st sheet Re 6o(t)/n c = 1.2/n, ß = 0.5 — Thiswork ♦ Carbonell&Karmanov -1.0 -0.5 0.0 0.5 ReVt 1.0 0.5 1.0 1.5 2.0 2.5 3.0 Im^/i Fig. 2. Left: Ground-state pole trajectory for ß = 4 as a function of the coupling [12]. Right: Phase shift of the leading partial wave compared to Ref. [16]. 0.8 0.6 0.4 0.2 0.0 deformations, the homogeneous BSE can be solved in the entire first sheet of the complex Vt plane [12]. The homogeneous BSE contains the full resonance information. However, extracting the resonance locations requires access to the second sheet, which is not directly possible from numerical solutions of the (in-)homogeneous BSEs and relies on analytic continuations methods such as the Schlessinger-point or Resonances-via-Pade method [21-23]. The strategy is then to solve the BSE on the first sheet (below and above the threshold) and determine the singularity structure on the second sheet by analytic continuation. Examples and results for the scalar model can be found in Ref. [12]. Another option, which does not require analytic continuation and provides direct access to the second sheet, is to solve the scattering equation for the four-point function at the bottom of Fig. 1. From the scattering equation one derives the two-body unitarity relation, which yields a self-consistent relation between the amplitudes on the first and second sheet. In other words, when solving the scattering equation the information on the second sheet, including the singularity structure of the amplitude, comes for free. In turn, one has to deal with more complicated contour deformations and first solve the half-offshell scattering equation, from where the onshell scattering amplitude, where all four external legs are on their mass shells, is extracted afterwards [12]. The left panel in Fig. 2 shows the resulting ground-state pole trajectory in the complex Vt plane determined from the scattering equation. It turns out that the model does not produce resonances but instead virtual states on the imaginary %/t axis (or negative t axis) of the second sheet. If one increases the coupling c starting at c = 0, the pole moves up to the threshold until it turns over to the first sheet, where the state becomes bound. When increasing the coupling further, the pole slides down on the first sheet until it eventually becomes tachyonic. The same pattern is repeated for excited states. The contour-deformation technique also allows one to extract phase shifts, which are related to the partial-wave amplitudes at Re%/t = 0 and ImVt > 1 8 Gernot Eichmann in a partial-wave expansion of the onshell scattering amplitude. The right panel in Fig. 2 shows the resulting phase shift for the leading partial wave. We cannot extract the phase shifts directly on the imaginary axis because here the deformed contour lies along a cut; instead we calculate it along lines in the complex %/t plane with Re%/t fixed and approaching the imaginary axis. The results are compared to those in Ref. [16], where the authors employed a Minkowski-space approach to determine the phase shift for the same parameter set in the scalar model. Although moving closer to the axis requires increasingly better numerics, there is satisfactory agreement between the two approaches. In summary, contour deformations provide a practical toolkit for treating resonances with integral equations. The formalism can be taken over without changes to systems with spin, such as Nn or NN scattering. Moreover, contour deformations are generally applicable for circumventing singularities in integrals and integral equations — e.g. in QCD, where the singularities of the quark propagator and other Green functions usually prohibit access to highly excited states, timelike form factors or form factors at large Q2. Acknowledgments: I would like to thank my collaborators Pedro Duarte, Teresa Pena and Alfred Stadler, and I am grateful to the organizers of the Bled 2019 Workshop for an enjoyable stay. This work was funded by the FCT Investigator Grant IF/00898/2015. References 1. I. C. Cloet and C. D. Roberts, Prog. Part. Nucl. Phys. 77 (2014) 1-69 2. G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer, and C. S. Fischer, Prog. Part. Nucl. Phys. 91 (2016) 1-100 3. H. Sanchis-Alepuz and R. Williams, Comput. Phys. Commun. 232 (2018) 1-21 4. P. Maris, Phys. Rev. D52 (1995) 6087-6097 5. S. Strauss, C. S. Fischer, and C. Kellermann, Phys. Rev. Lett. 109 (2012) 252001 6. A. Windisch, R. Alkofer, G. Haase, and M. Liebmann, Comput. Phys. Commun. 184 (2013) 109-116 7. A. Windisch, M. Q. Huber, and R. Alkofer, Phys. Rev. D87 (2013) no. 6, 065005 8. J. M. Pawlowski, N. Strodthoff, and N. Wink, Phys. Rev. D98 (2018) no. 7, 074008 9. R. Williams, Phys. Lett. B798 (2019) 276-280 10. A. S. Miramontes and H. Sanchis-Alepuz, 1906.0 6227[hep-ph] 11. E. Weil, G. Eichmann, C. S. Fischer, and R. Williams, Phys. Rev. D96 (2017) no. 1,014021 12. G. Eichmann, P. Duarte, M. T. Pena, and A. Stadler, 1907.05402[hep-ph] 13. K. Kusaka and A. G. Williams, Phys. Rev. D51 (1995) 7026-7039 14. V. Sauli and J. Adam, Jr., Phys. Rev. D67 (2003) 085007 15. T. Frederico, G. Salme, and M. Viviani, Phys. Rev. D89 (2014) 016010 16. J. Carbonell and V. A. Karmanov, Phys. Rev. D90 (2014) no. 5, 056002 17. S. Leitao, Y. Li, P. Maris, M. T. Pena, A. Stadler, J. P. Vary, and E. P. Biernat, Eur. Phys. J. C77 (2017) no. 10, 696 18. G. C. Wick, Phys. Rev. 96 (1954) 1124-1134 19. R. E. Cutkosky, Phys. Rev. 96 (1954) 1135-1141 20. N. Nakanishi, Prog. Theor. Phys. Suppl. 43 (1969) 1-81 21. L. Schlessinger, Phys. Rev. 167 (1968) 1411 22. I. Haritan and N. Moiseyev, J. Chem. Phys. 147 (2017) 014101 23. R.-A. Tripolt, I. Haritan, J. Wambach, and N. Moiseyev, Phys. Lett. B774 (2017) 411-416 Bled Workshops in Physics Vol. 20, No. 1 p. 9 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Flavor Mixing, Neutrino Oscillations and Neutrino Masses Harald Fritzsch Department für Physik, Universität München, Theresienstraße 37, D-80333 München, Germany Abstract. We discuss mass matrices with four texture zeros for the quarks and leptons. The three flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The results agree with the experimental data. The texture zero mass matrices for the leptons and the see-saw mechanism are used to calculate the matrix elements of the lepton mixing matrix as functions of the lepton masses. The neutrino masses are calculated: mi « 1.4 meV, m2 ~ 9 meV, m3 « 51 meV. The neutrinoless double beta decay is discussed. The effective Majorana neutrino mass, describing the double beta decay, can be calculated - it is about 5 meV. The present experimental limit is 140 meV. The flavor mixing of the quarks is described by the CKM matrix: Vub \ Vcb I . (1) VtJ The absolute values of the nine matrix elements have been measured in many experiments: ( 0.974 0.224 0.004 \ Uckm=* ( 0.218 0.997 0.042 I . (2) V 0.008 0.040 1.019/ There are several ways to describe the CKM-matrix in terms of three angles and one phase parameter. I prefer the parametrization, which Z. Xing and I introduced years ago (ref. [1]), given by the angles 9U, 0d, 0 and a phase parameter which describes CP violation: ( Cu Su 0\ ( e-^ 0 0\ (cd -sd 0\ Vckm = ( -Su Cu 0 I X ( 0 C S I X ( Sd Cd 0 I . (3) 0 0 1 0 -s c 0 0 1 Here we used the short notation: cu d ~ cos 0u d, su d ~ sin 0u d, c ~ cos 0 and s ~ sin 0. Relations between the quark masses and the mixing angles can be derived, if the quark mass matrices have "texture zeros", as shown by S. Weinberg and me /Vud Vus Vckm = I Vcd Vcs \Vtd Vts 10 Harald Fritzsch in 1977 (ref. [2]). For six quarks the mass matrices have four "texture zeros": 0 A0 \ M = | A* 0 B I . (4) 0 B* C) We can now calculate the angles 0u and 0d as functions of the mass eigenvalues: _ 0d - \/md/ms> 0u - Vmu/mc (5) Using the observed masses for the quarks, we find for these angles: ed ~ (13.0 ± 0.4)°, eu ~ (5.0 ± 0.7)°. (6) The experimental values agree with the theoretical results: ed ~ (11.7 ± 2.6)°, eu ~ (5.4 ± 1.1)°. (7) There is a relation between the four heavy quark masses and Vcb : Vcb = \Jms/mb mc/mt- (8) We use the following values for the quark masses: ms - 0.08 GeV, mb - 4.7 GeV, mc - 1.3 GeV, mt - 172 GeV. (9) In this case we find Vcb = 0.043. This value agrees with the experimental result: 0.039 < Vcb < 0.043. In the Standard Theory of particle physics the neutrinos do not have a mass. But a mass term can be introduced analogous to the mass term for the electrons. Nevertheless the masses of the neutrinos must be very small, much smaller than the mass of the electron. According to the limit from cosmology the sum of the neutrino masses must be less than 0.23 eV. If the neutrinos have a small mass and if they are superpositions of mass eigenstates, there would be also a flavor mixing of the leptons. An electron neutrino, emitted from a nucleus, can turn into a muon neutrino after travelling a certain distance. Afterwards it would again become an electron neutrino, etc. These neutrino oscillations were first discussed by P. Minkowski and me in 1975 (see ref. [3]). The flavor mixing of the leptons is described by a unitary 3x3-matrix, which is similar to the CKM-matrix for the quarks: (Uel Ue2 Ue3 \ U = | U^ U^ U^3 I . (10) \UTl Ut2 UT3 J This matrix can be described by three angles and a phase parameter. Here we use the standard parametrization, given by the three angles 012, 013 and 023. The phase parameter describes the CP-violation. Flavor Mixing, Neutrino Oscillations and Neutrino Masses 11 In the nuclear fusion on the sun many electron neutrinos are produced. In 1963 John Bahcall calculated the flux of the solar neutrinos. He concluded that this flux could be measured by experiments. Raymond Davis prepared such an experiment. It was placed in the Homestake Gold Mine in Lead, South Dakota and took data from 1970 until 1994. One observed only about 1/3 of the flux, calculated by Bahcall. Thus there were problems with the solar neutrinos, or the calculation of the flux by Bahcall was wrong. Today we know that the reduction of the solar neutrino flux is due to neutrino oscillations. In the Japanese Alps, near the small village "Kamioka", a big detector was built in 1982. It is located about 1000 m underground. This detector "Kamiokande" was built in order to find the hypothetical decay of a proton. Thus far no proton decay has been observed, but the detector can also be used to study neutrinos, in particular the atmospheric neutrinos, produced by the decay of pions in the upper atmosphere. In 1996 a new detector "Superkamiokande" started to investigate these neutrinos. This detector consists of a water tank, containing 50 000 liters of purified water, surrounded by about 11 000 photo multipliers. With this detector one could measure the flux of the neutrinos. The flux of neutrinos, coming from the atmosphere above Kamioka, was as high as expected, but the flux of the neutrinos, coming from the other side of the earth, was only about 50% of the expected rate. Afterwards a neutrino beam, sent from the KEK laboratory near Tsukuba towards Kamioka, was investigated. Again the flux of muon neutrinos was less than expected. Oscillations between the muon neutrinos and the tau neutrinos could explain the observed reduction of the flux. These oscillations are described by the angle 023. According to the experiments this angle is very large: In Canada a neutrino detector was built near Sudbury (Ontario), the Sudbury Neutrino Observatory (SNO). With this detector one could observe the solar neutrinos. An solar neutrino hits a deuteron, which splits up into two protons and an electron - this process can be observed. Furthermore it was possible to observe the neutral current interaction of the neutrinos. If a solar neutrino collides with a deuteron, it splits up into a proton and a neutron. Also this reaction can be observed. The neutral current interaction is not affected by oscillations, since all neutrinos have the same neutral current interaction. However oscillations can be observed for the charged current interaction. An electron neutrino, which becomes a muon neutrino, will not produce an electron after colliding with a nucleus. By comparing the interaction rates for the neutral and for the charged current interactions one has observed the oscillations of the solar neutrinos. For the corresponding mixing angle 012 one finds: 40,3° < e23 < 52,4°. (11) 31,6° < e12 < 36,3°. (12) Nuclear reactors emit electron antineutrinos. These neutrinos have been investigated at a few nuclear reactors, e,g, at the CHOOZ reactor in Belgium and 12 Harald Fritzsch afterwards at the Daia Bay reactors in China. Here neutrino oscillations have been observed, and one could measure the mixing angle 013: 8,2° < 913 < 9,0°. (13) Also the two small mass differences between the three neutrinos have been measured. The mass difference between the first and the second neutrino is about 0.0086 eV, and the mass difference between the second and the third neutrino is about 0.05 eV. Using the measured mixing angles, we can calculate the mixing matrix for the leptons. The mixing matrix of the quarks is close to the unit matrix, since the mixing angles are small. However this is not the case for the leptons, since two of the mixing angles are large. Thus the mixing matrix of the leptons is quite different from the mixing matrix of the quarks. Thus far it is not clear, how large the CP-violation is for the leptons. A violation of this symmetry implies, that the oscillation of two neutrinos is different from the oscillation of the corresponding antineutrinos. For example, the oscillation between electron neutrinos and muon neutrinos would be different form the oscillation between electron antineutrinos and muon antineutrinos. The results from the experiment T2K in Japan indicate that there might be a large CP-violation. In 2027 two new experiments will start to measure CP-violation. At Fermi-lab the new experiment DUNE ("Deep Underground Neutrino Experiment") is prepared. In Japan the new experiment "Hyper-Kamiokande" will start in 2027. Thus in about 10 years we shall know, whether there is a large CP-violation for leptons. The neutrino masses are very small, and the question arises, if the neutrino masses are different from the Dirac masses of the charged leptons. Since the neutrinos are neutral, the neutrino masses might be Majorana masses. The smallness of the neutrino masses can be understood by the "seesaw"-mechanism. The mass matrix of the neutrinos is a matrix with one "texture zero" in the (1,1)-position. The two off-diagonal terms are given by the Dirac mass term D - a large Majorana mass term is in the (2,2)-position: Mv=(DM )■ (14) After diagonalization one obtains a large Majorana mass M and a small neutrino mass: mv ~ D2/M. (15) Now we assume that the Dirac mass matrices of the leptons also have four texture zeros: (16) 0 A 0 A* 0 C 0 C* D D Flavor Mixing, Neutrino Oscillations and Neutrino Masses 13 In the seesaw formula we replace the Dirac mass by the texture zero mass matrix MD and the Majorana mass by a Majorana mass matrix MD: Mv = MDM-1Md . (17) Since the Majorana masses are much larger than the masses of the leptons and quarks, we assume, that the Majorana mass matrix is proportional to the unit matrix. In this case the mixing angles are functions of the ratios of the charged lepton masses and of the neutrino masses. But the mass ratios of the charged leptons are very small and cannot give large mixing angles. These angles must be related to large ratios of the neutrino masses (ref. [4,5,6,7]). In first approximation we can neglect the mass ratios of the charged leptons and can calculate the matrix elements of the mixing matrix, in the particular those matrix elements, mentioned below: / \ 1/4 = 2 1= (IS ) , 1/4 ^ i=(m) ■ / N 1/2 ✓ \ 1/2 ^(m) (mi) ■ ™ We use these relations and the experimental results for the mixing angles to determine the three neutrino masses: m1 ~ 1.4 meV, m2 ~ 9 meV, m3 ~ 51 meV. (19) One expects that the Dirac term D is similar to the corresponding charged lepton mass. For example, let us consider the tau lepton and its neutrino. If D is given by the tau lepton mass and the corresponding neutrino mass is 51 meV, we obtain for the heavy Majorana mass M: M ~ 6.3 x 1010 GeV. (20) The only way to test the nature of the neutrino masses is to study the neutri-noless double beta decay, which violates lepton number conservation. Two neutrons inside an atomic nucleus decay by emitting two electrons and two neutrinos. The two Majorana neutrinos annihilate - only two electrons are emitted. The annihilation rate is a function of the Majorana mass of the neutrino. If neutrinos mix, all three neutrino masses will contribute to the decay rate. Their contributions are given by the masses of the neutrinos and by the mixing angles. Using the neutrino masses and the observed mixing angles, one finds for the effective neutrino mass, relevant for the neutrinoless double beta decay: m ~ 5 meV. (21) 14 Harald Fritzsch In various experiments one has searched for the neutrinoless double beta decay, for example for the decay of tellurium. Thus far the decay has not been observed. Here is the present limit for this effective mass, given by the Cuore and the Gerda experiments in the Gran Sasso Laboratory: m <140 meV. (22) This limit is about thirty times larger than the expected value. In 2025 a new detector will be ready: "LEGEND" ("Large Enriched Germanium Experiment for Neutrinoless Double-Beta Decay"). This detector will be able to establish a new limit for the effective neutrino mass, about 1 meV. Since I expect about 5 meV for this mass, I predict that the neutrinoless double beta decay will be discovered with this detector. Conclusions: Using 4 texture zeros for the mass matrices of the quarks and leptons, we derived relatons between the flavor mixing angles and the mass ratios of the leptons and quarks. For the quarks the results agree with the experimental values. Using the observed mixing angles of the leptons, we calculated the three neutrino masses. The effective neutrino mass, describing the neutrinoless double beta decay, is much smaller than the present limit of the experiments. The neutrinoless double beta decay will be observed after 2025 with the new detector "LEGEND". References 1. H. Fritzsch and Z. Z. Xing, Phys. Lett. B 413, (1997) 396, H. Fritzsch and Z. Z. Xing, Phys. Rev. D 57, 594 (1998). 2. H. Fritzsch, Phys. Lett. 70B (1977) 436, S. Weinberg, Trans. New York Acad. Sci. 38,185 (1977), H. Fritzsch, Phys. Lett. 73B (1978) 317. 3. H. Fritzsch and P. Minkowski, Phys. Lett. B 62 (1976) 76 . 4. M. Fukugita, M. Tanimoto, T. Yanagida, Prog.Theor.Phys. 89 (1993) 263. 5. Z. Xing, Phys.Lett. B550 (2002) 178. 6. M. Fukugita, M. Tanimoto, T. Yanagida, Phys.Lett. B562 (2003) 273. 7. M. Fukugita, Y. Shimizu, M. Tanimoto, T. Yanagida, Phys.Lett. B716 (2012) 294. Bled Workshops in Physics Vol. 20, No. 1 p. 15 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Hidden Charm Molecular Pentaquarks: Some Open Questions Marek Karliner School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Abstract. LHCb has recently reported three narrow states in —> J/^pK- decays, Pc(4312), Pc(4440) and Pc(4457), decaying into J/^p, i.e., having minimal quark content ccuud. Two states are slightly below ZcD* threshold and one state is slightly below the ZcD threshold. This is highly suggestive of hadronic molecules and immediately triggers some intriguing follow-up questions. The relevant issues which seem interesting to me include • Four additional Pc states with I£ instead of Ic: I*D and I*Dc? • Decay of Pc-s into AcD? • So far no signal of Pc-s in yp —» J/^p photoproduction • If Pc(4312) is a IcD molecule, why don't we see a DD molecule? • Why are Pc binding energies ^ other hidden-charm hadronic molecules? • Pc (4440) and Pc (4457): likely IcDc, S = f, f 17 MeV spin splitting ^ deuteron (S=1 ) vs. pn S=0 • What can we learn about the Pc-s from the lattice? In the following I discuss several of these questions in some detail. Four additional L* D(D*) molecules? Three narrow Pc states have recently been reported by LHCb [1]. The state Pc(4312) is just a few MeV below IcD threshold, and is a natural candidate for a IcD molecule. Similarly, the states Pc(4440) and Pc(4457) are natural candidates for IcD* molecules, one with spin 1 and the other with spin | (we don't know which is which yet). In the mc —» oo limit the Ic and ic baryons are degenerate. So are the D and D* mesons. Therefore in the heavy quark limit one expects I* to form molecules by binding with D and D *. In this limit the only difference is that ic has spin |, so there is one I*D molecule with spin f and there are three icD* molecules, with S=1, f, f. In the real world, however, ic is about 36 MeV heavier than Ic and has a significantly shorter lifetime, r(ic) « 15 MeV - r(Pc), vs. r(Ic) « 2 MeV. As a 16 Marek Karliner general rule it only makes sense to talk about a bound state if the lifetime of the constituents is significantly longer than the lifetime of a bound state. A LcD(*' molecule is therefore a borderline case. This issue should be investigated carefully from the theoretical point of view, and of course it will be extremely interesting to see whether such states are observed experimentally. Additional decay mode Pc -> ACD(D*)? The (ccuud) quark content of the Pc states at 4312, 4440, 4457 MeV is the same as that of AcD and AcD*. Both are well below the Pc masses, m(Ac) + m(D° ) = 4150 MeV, m(Ac) + m(D°*) = 4293 MeV. Spin & parity conservation allow the decays (IcD*,S=3) -> AcD*, (IcD*,S=1) -> AcD, AcD*, (IcD,S=1) -> AcD, AcD*. Unlike in the decay to J/^p, the IcDmolecules can decay to AcDwith-out having to bring the charmed and anticharmed quarks close to each other. Therefore it is likely that |(Pc|AcD(D*))|2 > |(PclJ/^p)|2, so we expect r(Pc -> AcD(*' > r(Pc —» J^p). This immediately brings up the question why AcD(D*) decays have not been not seen? This question is discussed below. Why has Pc —» AcD° not been seen? Most likely this an experimental issue in LHCb: a product of several small BR-s, large number of charged tracks and background rejection. Compare Pc —» J/^p and Pc —» AcD°. J/^ is identified by its dimuon decay, BR(J/^ —> M-+M--) = 6%, so finally Pc —> i.e. 3 charged tracks. On the other hand, in Pc -> AcD° BR(Ac -> K-pn+) = 6.28%, BR(D° ^ K+n-) = 4%, so BR(...) xBR(...) = 0.25%, with 5 charged tracks. Each additional charged track comes with an efficiency penalty, so detection efficiency x BR for the all charged final state in Pc —» Ac D° is much smaller. Why Pc -> AcD*° hasn't been seen? On top of AcD° issues, D* needs to be identified through its characteristic decays D*° —» D°n° or D*° —> D°y. These decays necessitate identification of soft n° or y, both of which have rather low efficiency in LHCb. The upshot is Pc —» AcD°(D*°) should eventually be seen, but with much more data. The hierarchy of partial widths, BR(Pc -> AcD(D*)) > BR(Pc -> J/^p) suggests a relatively small coupling in yp —» Pc —> J/^p, relevant for the photoproduction experiments. Why no signal of Pc-s in yp —> J/^p photoproduction? For obvious reasons it is essential to confirm the LHCb findings and to observe the Pc resonances in another experiment. At the moment no other experiment has a comparable number of Ab-s and a suitable detector in order to repeat the Hidden Charm Molecular Pentaquarks: Some Open Questions 17 LHCb analysis in the same channel. Instead, several groups proposed to look for Pc(4450) as an s-channel resonance in photoproduction, yp —» J/^p [4-6]. In fixed target mode the required energy of the photon is about 10 GeV. Several fixed-target experiments are currently under way at JLab. The first results have recently been published by GlueX Collaboration [7]. They do not see the relevant resonances in the yp channel and are able to set model-dependent upper limits on their branching fractions B(P+ —» J/^p) and cross sections u(yp —» P+)xB(P+ —» J/^p). The most likely explanation, within the molecular model, is that the Pc —» J/^p partial width is rather small, much smaller than Pc —» AcDas discussed above. But eventually, with sufficient integrated luminosity, the yp —» Pc —» J/^p process should be seen. In principle it is also possible to look for a bottom analogue of Pc(4450), a !bB* molecule around 7.778 GeV in the reaction yp —» Yp. But since the required lab photon energy is 65.7 GeV, it is far from clear that such an experiment is feasible. pc -> nc p? This channel is expected in addition to Pc —» J^p and Pc —> AcD0(*'. Since nc has JP = 0-, only Pc states with S = 2 can decay through this channel. Detection is difficult. The quark spin wave function for D*°TT, S=1: (c^u^d^) (c^u^) implies decay to is preferred, while for IcD no preference is expected for J/-^(cTcT) overnc(cTc^). If Pc(4312) is a £cD molecule, why no DD molecule? Hadronic molecules consist of two color-singlet hadrons, which are analogous to proton and neutron in a deuteron. Binding is provided by exchange of light mesons. The lightest meson is the pion, so one expects that one-pion exchange plays a significant role in generating the necessary attraction. This immediately explains why we observe DD* [X(3872) and Zc(3900)] and D*D* [Zc(4020)], as well as BB* [Zb(10610)] and B*B* [Zb(10650)] hadronic molecules, but not DD, nor BB. The reason for absence of DD and BB is that parity and angular momentum conservation forbid a three-pseudoscalar vertex like D-D-n. So DD cannot bind by exchanging one pion. The same logic suggests one-pion exchange can bind a IcD* molecule, but not a IcD molecule [2]. But Pc(4312) very much looks like a IcD molecule. So what mechanism binds IcD, but does not bind DD? What binds IcD but not DD? If one-pion exchange is impossible, the next obvious thing to look at is two-pion exchange, illustrated in Fig. 1. In DD system, shown in Fig. 1(a), the intermediate state consists of D*D*, which is 284 MeV heavier than DD. This is a very large energy denominator, and consequently two-pion exchange does not contribute to DD binding. The situation is dramatically different in IcD system, shown in 18 Marek Karliner (a) D AM= +142 MeV D* D D * AM = +142 MeV D D (b) AM = -167 MeV S Ac D AM= D * +142 MeV Sc D Fig. 1. Two-pion exchange diagrams for (a) DD (b) ZcD. The intermediate states are denoted, together with AM, the mass difference from the original hadron. Fig. 1(b). There the intermediate system consists of AcD*. The crucial difference from DD is that Ac is 167 MeV lighter than Ic. As a result, the intermediate AcD* state is only 25 MeV below IcD, instead of 284 MeV above in the DD case, and therefore in this case two-pion exchange does contribute to binding. In addition to this crucial difference, there are two additional factors which work in favor of IcD vs. DD: (a) Ic has I = 1 vs. D with I = 1, implying that Ic has a stronger coupling to light hadrons; (b) larger reduced mass: Mreduced(IcD)=1060 MeV > Mreduced(DD)=932 MeV, making the repulsive kinetic energy 12% smaller. It is not clear if this is the whole story, but the above do provide a suggestive binding mechanism. The alternative, advocated by Voloshin, is that "DD does exist, but hard to see" [3]. If a X(3872)-like DD exists, could it have evaded experiments? In my opinion this is very unlikely. Such a X(3872)-like D0D0 molecule X(3729) would lie close to the threshold at 3729 MeV, have JPC = 0++, and be a mixture of I = 0 and I = 1. Its production mechanisms would be analogous to X(3872) and xc0, B -> KX(3729), cf. B -> KX(3872); e+e- —» yX(3729), cf. e+e- —» YXc0. Expected decay modes are X(3729)-> J/^p, J/^y, ^'Y. These are right in LHCb, BESIII, BaBar and Belle courts, but no such state has been reported. Why Pc binding energies ^ other hidden-charm molecules? X(3872) lies < 1 MeV from DD* threshold, Zc(3900) and Zc(4020) are above the D°D+* and D0*D+* thresholds, For comparison, the deuteron is 2.2 MeV below pn. So why are Pc-s 5 ^ 22 MeV below IcD (D*)? Hidden Charm Molecular Pentaquarks: Some Open Questions 19 Alternatively, why is their size so much smaller? Estimating the size from r « 1/^/2 ^Tedl AE|, where |j.Ted is the reduced mass and AE is the binding energy, we have for the deuteron size rd « 3 fm. Similarly, from AE(X(3872)) < 1 indicates that rx(3872) > 4.5 fm. These are to be compared with Pc (4312): r « 1.6 fm, Pc (4440): r « 0.9 fm, Pc (4457): r « 1.9 fm. 17 MeV spin splitting between Pc(4457) and Pc(4440) In the molecular model these two states are naturally interpreted as spin 1 and spin 2 IcD* molecules. There is one hadronic molecule where the spin splitting is known. This is the deuteron, which has spin 1. We know there is a spin-0 p n state just above threshold. So the spin splitting for the deuteron is ~ 2.2 MeV C 17 MeV that we see here. This is probably related to the deeper binding and smaller size discussed above. Spin-spin interaction is usually short range, so having a smaller molecule enhances the splitting. An obvious difference between the Pc and the meson-meson hadronic molecules with hidden charm is the fact that Ic has I=1 and is heavier than the charmed mesons. Both of these enhance the net attraction. Hopefully detailed calculations in specific models can elucidate this question and show if these are sufficient to generate the observed larger binding and spin splitting. Acknowledgements The original results referred to in this talk were obtained in collaboration with Jon Rosner. I wish to thank the organizers of the 2019 Bled Mini-Workshop for creating a stimulating environment for discussions of current problems in hadronic physics. The references appearing below are not meant assign credit where it belongs, but rather to help the reader in locating the specific additional background that might needed. Extensive sets of references can be found in recent reviews, e.g., [8] and [9]. References 1. R. Aaij et al [LHCb Collaboration], Phys. Rev. Lett. 122, 222001 (2019) [arXiv:1904.03947 [hep-ex]]. 2. M. Karliner and J. L. Rosner, Phys. Rev. Lett. 115,122001 (2015) [arXiv:1506.06386 [hep-ph]]. 3. M. Voloshin, private communication. 4. Q. Wang, X. H. Liu and Q. Zhao, Phys. Rev. D 92, 034022 (2015) [arXiv:1508.00339 [hep-ph]]. 20 Marek Karliner 5. V. Kubarovsky and M. B. Voloshin, Phys. Rev. D 92, 031502 (2015) [arXiv:1508.00888 [hep-ph]]. 6. M. Karliner and J. L. Rosner, Phys. Lett. B 752, 329 (2016) [arXiv:1508.01496 [hep-ph]]. 7. A. Ali et al [GlueX Collaboration], Phys. Rev. Lett. 123, no. 7, 072001 (2019) doi:10.1103/PhysRevLett.123.072001 [arXiv:1905.10811 [nucl-ex]]. 8. S. L. Olsen, T. Skwarnicki and D. Zieminska, Rev. Mod. Phys. 90, 015003 (2018) [arXiv:1708.04012 [hep-ph]]. 9. M. Karliner, J.L. Rosner and T. Skwarnicki, Ann. Rev. Nucl. Part. Sci. 68,17 (2018) [arXiv:1711.10626 [hep-ph]]. Bled Workshops in Physics Vol. 20, No. 1 p. 21 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 A unified approach for the structure of light and heavy baryons Hyun-Chul Kim Department of Physics, Inha University, Incheon 22212, Republic of Korea, School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea Abstract. In the present talk, we summarize a series of recent works on the structure of light and heavy baryons, based on the chiral quark-soliton model. The present summary can be considered as a brief guide to the model. For details, we refer to the references given. 1. The chiral quark-soliton model (xQSM), which was constructed as a pion mean-field theory for the structure of the nucleon many years ago [1], has been successfully applied to the description of not only low-lying SU(3) hyperons but also singly heavy baryons (See the following reviews [2-4]). The xQSM was mainly motivated by Witten's seminal works [5,6], in which a baryon can be considered as a system consisting of Nc valence quarks bound by meson mean fields. Here, Nc denotes the number of colors. This is justified in the large Nc limit. In this limit, the nucleon mass is proportional to Nc whereas its width is of order O(1). Mesons are weakly interacting and the meson-loop fluctuations are suppressed by 1/Nc. The starting point of the xQSM is the effective chiral action given as Seff[na ] = —NcTrln(i/ + iMUY5 + im), (1) where the chiral field UY5 is defined as UY5 := exp(inaAaY5) = U(x) Pr + U(x)f Pl. (2) PR and PL denote the projection operators defined by PR = (1 + y5)/2 and PL = (1 — Y5)/2. m designates the current quark mass matrix: m := diag(mu, md,ms) = m01 + m3A3 + m8A8 .When isospin symmetry is imposed, m3 is set equal to zero m3 = (mu — md)/2. The Tr represents the functional trace over the space-time and all internal spaces. The effective chiral action in Eq. (2) can be derived from the low-energy QCD partition function through the instanton vacuum [7,?]. While the original one contains the momentum-dependent dynamical quark mass M(p), which arises from the Fourier transform of the fermionic zero modes, we turn off the momentum dependence, so the dynamical quark mass M becomes constant as in Eq. (2). However, we have to pay the price for taking the constant M: the 22 Hyun-Chul Kim regularization of the quark loop. The value of the cut-off mass for the regular-ization is fixed by reproducing the experimental data of the pion decay constant. The up or down quark mass is determined by the experimental value of the pion mass. Thus, the only remaining free parameter in this model is the value of the dynamical quark mass. However, its value will be determined to be around 420 MeV by computing the charge radius of the proton. The presence of Nc valence quarks in this large Nc limit, which consist of the lowest-lying baryons, produce the pion mean fields by which they are influenced self-consistently. This picture is very similar to a Hartree approximation in many-body theories. Explicitly, we start from a trial solution of the classical equation of motion and derive the eigenenergies and eigenvectors of the one-body Dirac equation. Using these results, we obtain a new profile of the chiral soliton or the mean-field solution. We repeat this procedure till the classical soliton energy is reached to a converged value. We identify this energy as a classial mass of the soliton. The next step is the collective quantization of the classical soliton. Since the soliton does not have rotational and translational symmetries, we restore this symmetries by using the zero-mode quantization. Then the nucleon and lowest-lying hyperons arise as rotational collective states. 2. We can apply exactly the same procedure to singly heavy baryon systems. A singly heavy baryon contains a pair of light quarks and a heavy quark. Since the mass of the heavy quark is much heavier than that of a light quark, one can consider the infinitely heavy quark mass limit, i.e. mQ —» oo. In this limit, the spin of the heavy quark is conserved, since the infinitely heavy mass does not allow the spin of the quark to be flipped. It leads to the conservation of the total spin of light quarks: JL = J — Jq, where JL, Jq, and J stand for the spin of the light-quark pair, that of the heavy quark, and the total spin of the heavy baryon. This is coined as the heavy-quark spin symmetry that allows JL to be a good quantum number. Furthermore, the physics is kept intact under the placement of heavy quark flavors. This is known as the heavy-quark flavor symmetry [912]. Then the heavy quark becomes static, so that it can be considered as a static color source. It indicates that the heavy quark inside a singly heavy baryon can be stripped off from the baryon and the dynamics of the heavy baryon is mainly governed by the light quarks. The flavor structure of the heavy baryon also comes from the light-quark constituents. Since a singly heavy baryon contains two light quarks, there are two SUf (3) irreducible representations, i.e. 3 ( 3 = 3 © 6. The spatial part of the heavy-baryon ground state is symmetric due to the zero orbital angular momentum, so that the color part is totally antisymmetric to satisfy the generalized Pauli principle. Moreover, since the flavor anti-triplet (3) is antisymmrtric, the spin state of 3 should be antisymmetric. Thus, a baryon belonging to the anti-triplet should have JL = 0. By ths same token, the flavor-symmetric sextet (6) should be symmetric in spin space, i.e. JL = 1. This leads to the fact that the baryon antitriplet has spin J = 1/2, while the baryon sextet carries spin J = 1/2 or J = 3/2, with the spin of the light-quark pair being coupled with the heavy quark spin Jq = 1/2. So, we can classify 15 different lowest-lying heavy baryons as shown in Fig. 1 in the case of charmed baryons. The bottom baryons are also classified as shown A unified approach for the structure of light and heavy baryons 23 y y y /= 1/2 7 = 1/2 7 = 3/2 Fig. 1. The anti-triplet (3) and sextet (6) representations of the lowest-lying heavy baryons. The left panel draws the weight diagram for the anti-triplet with the total spin 2. The centered panel corresponds to that for the sextet with the total spin 1/2 and the right panel depicts that for the sextet with the total spin 3/2. in Fig. 1. The only difference of the bottom baryons is the charge of the bottom quark from that of the charm quark. The pion mean-field approach was developed in Ref. [13] to describe the masses of singly heavy baryons, being motivated by Ref. [14]. In fact, it is straightforward to extend the original mean-field approach to the singly heavy baryons in which we have Nc — 1 light valence quarks with the single heavy quark stripped off (Fig. 2). The presence of the Nc — 1 valence quarks will also create the pion mean fields in which they are bound by the pion mean fields self-consistently. Fig. 2. Schematic picture of a heavy baryon. The Nc — 1 valence quarks are filled in the lowest-lying valence level KP = 0+ with the heavy quark stripped off. KP denotes the grand spin which we will explain later and P is the corresponding parity of the level. The presence of the valence quarks will interact with the sea quarks filled in the Dirac sea each other. This interaction will bring about the pion mean field. The constraint right hyper charge is taken to be Y' = (Nc — 1 )/3 and allows the lowest-lying representations: the baryon anti-triplet (3), the baryon sextet (6), 24 Hyun-Chul Kim the baryon anti-decapentaplet (15). The model reproduced successfully the mass splitting of the baryon anti-triplet and sextet in both the charm and bottom sectors [13,15]. In addition, the mass of the baryon, which has not yet found, was predicted [16,16]. The magnetic moments baryons [18] and electromagnetic form factors [19] of the singly heavy baryons were also studied within the same framework. The xQSM was also used to interpret the five D.c baryons newly found by the LHCb Collaboration [16,17]. Within the present framework, two of the Hcs with the smaller widths are classified as the members of the baryon 15, whereas all other Hc's belong to the excited baryon sextet. The widths were quantitatively well reproduced without any free parameter. Acknowledgements I want to express my gratitude to the organizers of the wonderful Bled MiniWorkshop. I am very grateful to J.-Y. Kim, M. V. Polyakov, M. Praszaiowicz, and Gh.-S. Yang for fruitful collaborations and discussions. The present work is supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2018R1A2B2001752). References 1. D. Diakonov, V. Y. Petrov and P. V. Pobylitsa, Nucl. Phys. B 306, 809 (1988). 2. C. V. Christov, A. Blotz, H.-Ch. Kim, P. Pobylitsa, T. Watabe, T. Meissner, E. Ruiz Arriola and K. Goeke, Prog. Part. Nucl. Phys. 37, 91 (1996). 3. D. Diakonov, hep-ph/9802298. 4. H.-Ch. Kim, J. Korean Phys. Soc. 73, no. 2,165 (2018) [arXiv:1804.04393 [hep-ph]]. 5. E. Witten, Nucl. Phys. B 160, 57 (1979). 6. E. Witten, Nucl. Phys. B 223, 422 (1983) and Nucl. Phys. B 223, 433 (1983). 7. D. Diakonov and V. Y. Petrov, Nucl. Phys. B 245, 259 (1984). 8. D. Diakonov and V. Y. Petrov, Nucl. Phys. B 272, 457 (1986). 9. N. Isgur and M. B. Wise, Phys. Lett. B 232,113 (1989). 10. N. Isgur and M. B. Wise, Phys. Rev. Lett. 66,1130 (1991). 11. H. Georgi, Phys. Lett. B 240, 447 (1990). 12. A. V. Manohar and M. B. Wise, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10, 1 (2000). 13. Gh.-S. Yang, H.-Ch. Kim, M. V. Polyakov and M. Praszaiowicz, Phys. Rev. D 94,071502 (2016) 14. D. Diakonov, arXiv:1003.2157 [hep-ph]. 15. J. Y. Kim, H.-Ch. Kim and G. S. Yang, arXiv:1801.09405 [hep-ph]. 16. H.-Ch. Kim, M. V. Polyakov and M. Praszaiowicz, Phys. Rev. D 96, no. 1, 014009 (2017) Addendum: [Phys. Rev. D 96, no. 3, 039902 (2017)] [arXiv:1704.04082 [hep-ph]]. 17. H.-Ch. Kim, M. V. Polyakov, M. Praszalowicz and G. S. Yang, Phys. Rev. D 96, no. 9, 094021 (2017) Erratum: [Phys. Rev. D 97, no. 3, 039901 (2018)] [arXiv:1709.04927 [hep-ph]]. 18. G. S. Yang and H. C. Kim, Phys. Lett. B 781, 601 (2018) doi:10.1016/j.physletb.2018.04. 042 [arXiv:1802.05416 [hep-ph]]. 19. J. Y. Kim and H.-Ch. Kim, arXiv:1803.04069 [hep-ph]. Bled Workshops in Physics Vol. 20, No. 1 p. 25 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Improved pion mean fields* June-Young Kima, Hyun-Chul Kima'b a Department of Physics, Inha University, Incheon 22212, Republic of Korea b School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea Abstract. In this presentation, we report recent results on improved pion mean fields within the chiral quark-soliton model. We investigate effects of the reduction of the number of the valence quarks from Nc to Nc — 1 and Nc — 2 on the pion mean fields, and their physical implications are discussed. 1 Introduction The light baryon has been studied within a pion mean-field approach in the limit of large Nc or the chiral quark-soliton model (xQSM) [1] over decades. The model has succeeded in describing the structure of the lowest-lying light baryons [2,3]. In a similar manner, the xQSM idea has been recently applied to the singly heavy baryon sector to investigate how the pion mean fields explain various properties of heavy baryons. The main idea is that heavy baryons consist of Nc — 1 light valence quark bound by the pion mean fields. While the sea-quark polarization is kept to be intact and the heavy quark is treated as a mere static color source in the limit of infinitely heavy quark mass, e.g. mQ —» oo, the contribution of the Nc — 1 light valence quarks are modified. By doing that, we were able to describe the properties of the singly heavy baryons [4,5]. However, the pion mean fields should explicitly be obtained by solving the classical equation of motion in the presence of the Nc — 1 valence quarks instead of Nc quarks. In this talk, we will present a recent work on how the pion mean fields can be modified by changing the number of the light valence quarks from Nc to Nc—N q, where NQ denotes the number of the heavy quarks. We find that indeed the pion mean fields undergo the changes by reducing the number of the light valence quarks. 2 Result and discussion The detailed formalism for solving the classical equation of motion within the present framework is presented in [6]. Fig. 1 depicts soliton mass as a function of the dynamical quark mass for the pion mean fields with the Nc valence quarks. In the presence of the Nc valence * Talk presented by June-Young Kim 26 June-Young Kim, Hyun-Chul Kim Nc light valence quarks 2500r 2000 „ 1500 a) looo ^ 500 o I en ^ 0 -500 -1000 Total Valence Sea 400 600 800 1000 1200 1400 MMeV] Fig. 1. Soliton mass as a function of the dynamical quark mass for the pion mean fields in the presence of the Nc valence quarks. The long-dashed line draws the valence-quark contribution, whereas the short-dashed one depicts the sea-quark contribution. The solid line represents the soliton mass. quarks, the solutions of the classical equation of motion exist when the dynamical quark mass M is larger than the critical mass Mcr « 350 MeV. Note that the dynamical quark mass M acts as a coupling between the pion and the quark. For that reason, the vacuum polarization becomes stronger as M increases. On the other hand, the strength of the interaction is not strong enough to get the Nc valence quarks being bound over the values of M below Mcr. In the meanwhile, even though sea- and valence-quark contributions vary noticeably with M, the classical mass is not much changed. When the value M reaches around 800 MeV, valence energy crosses into the negative energy. It indicates that, from that point, the soliton energy does solely come from the sea-quark contribution. Fig. 2 depicts soliton mass as a function of the dynamical quark mass for Nc — 1 mean fields. The Nc — 1 mean fields, singly heavy baryon, consist of Nc — 1 valence quarks and a heavy quark. It means that the number of the valence quarks is reduced by one. That is to say, the pion mean fields are weakened as much as the absence of the valence quark, which affects the vacuum polarization. As a result, the critical point of the dynamical quark mass is found to be Mcr « 400 MeV. By the same token, the vacuum is weakly polarized all over the region. The dependence of the dynamical quark mass of valence- and sea-quark energies is similar to the case of the Nc mean fields. Fig. 3 presents the values of the soliton mass for the pion mean fields in the presence of the Nc — 2 valence quarks, as a function of M. Note that in this case the soliton consists of only a single valence quark, we do not find any stabilized soliton till M is reached to Mcr « 600 MeV. It indicates that the present framework is not suitable to study doubly heavy baryons. Improved pion mean fields 27 Nc — 1 light valence quarks Total Valence Sea 2500i 2000 „ 1500 a) looo _____________ ^ 500 , s ~~~ —■ ^ °-- -500 -1000 400 600 800 1000 1200 1400 MMeV] Fig. 2. Soliton mass as a function of the dynamical quark mass for the pion mean fields in the presence of the Nc — 1 valence quarks. The long-dashed line draws the valence-quark contribution, whereas the short-dashed one depicts the sea-quark contribution. The solid line represents the soliton mass. Nc - 2 light valence quarks 1750 1500 >1250 N200, /3=3.55(b) > N401, /3=3.46(d) o D200, /3=3.55(b) o J303, /3=3.7(c) ms = mud r M=a r M=b r M=0 r M=0.6b r M=0.4b r M=0.2b ms=0 Light- and strange-quark mass dependence of the p(770) meson properties 41 mn (MeV) mn (MeV) Fig. 9. Top: couplings of the rho meson to the nn channel in different chiral trajectories; Bottom: the ratio gKK/gnn in different chiral trajectories. ward to investigate more on these chiral trajectories, which indeed provide useful information to push forward the field. 5 Acknowledgements This work is partly supported by the Talento Program of the Community of Madrid and the Complutense University of Madrid, under the project with Ref. 2018-T1/TIC-11167. R.M. acknowledges financial support from the Fundacao de amparo a pesquisa do estado de Sao Paulo (FAPESP), processo No. 2017/02534-3. R. M. also acknowledges discussions with C. Bernard, S. Schaefer, M. Bruno, and to the MILC Collaboration, and J. Bulava for providing the data. 42 R. Molina, J. Ruiz de Elvira References 1. M. Bruno, T. Korzec and S. Schaefer, Phys. Rev. D 95 (2017) no.7, 074504 2. C. Andersen, J. Bulava, B. Horz and C. Morningstar, Nucl. Phys. B 939 (2019) 145 3. T. Blum et al. [RBC and UKQCD Collaborations], Phys. Rev. D 93 (2016) no.7, 074505 4. A. Bazavov et al. [MILC Collaboration], PoS LATTICE 2010 (2010) 074 5. A. Bazavov et al. [MILC Collaboration], Rev. Mod. Phys. 82 (2010) 1349 6. C. Aubin, J. Laiho and R. S. Van de Water, PoS LATTICE 2008 (2008) 105 7. J. J. Dudek et al. [Hadron Spectrum Collaboration], Phys. Rev. D 87 (2013) no.3, 034505 Erratum: [Phys. Rev. D 90 (2014) no.9, 099902] 8. D. J. Wilson, R. A. Briceno, J. J. Dudek, R. G. Edwards and C. E. Thomas, Phys. Rev. D 92 (2015) no.9, 094502 9. J. Bulava, B. Fahy, B. Horz, K. J. Juge, C. Morningstar and C. H. Wong, Nucl. Phys. B 910 (2016) 842 10. T. N. Truong, Phys. Rev. Lett. 61 (1988) 2526. 11. J. Gasser and H. Leutwyler, Annals Phys. 158 (1984) 142. 12. J. Gasser and H. Leutwyler, Nucl. Phys. B 250 (1985) 465. 13. A. Gomez Nicola and J. R. Pelaez, Phys. Rev. D 65 (2002) 054009 14. J. Nebreda and J. R. Pelaez., Phys. Rev. D 81 (2010) 054035 15. B. Hu, R. Molina, M. Doring and A. Alexandru, Phys. Rev. Lett. 117, no. 12, 122001 (2016) 16. B. Hu, R. Molina, M. Doring, M. Mai and A. Alexandru, Phys. Rev. D 96 (2017) no.3, 034520 17. S. Aoki et al. [Flavour Lattice Averaging Group], arXiv:1902.08191 [hep-lat]. 18. D. Guo, A. Alexandru, R. Molina and M. Doring, Phys. Rev. D 94 (2016) no.3, 034501 Bled Workshops in Physics Vol. 20, No. 1 p. 43 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Electromagnetic Form Factors of the Nucleons, the A, and the Hyperons W. Plessas Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria Abstract. We discuss the electromagnetic structures of baryons on the basis of a unified relativistic constituent quark model. After recalling the covariant nucleon elastic form factors including their flavor decompositions we continue on the same route towards the A, A, Z, and Q form factors. Specific features of elastic electromagnetic form factors of baryons belonging to either octet or decuplet flavor multiplets are exemplified. In order to be meaningful and comprehensively applicable, any effective tool for the description of low-energy hadronic physics has not only to reproduce the hadron spectroscopy but must also correctly provide for the hadron structures as seen in reactions with external probes. Nowadays we have a wealth of experimental data especially from electron scattering, which put stringent tests on electromagnetic form factors. This is particularly true for the nucleons, as one has gained specific insights into the flavor compositions of both the proton and neutron elastic form factors [1-4]. For now almost two decades the Graz group has studied the electroweak structures of baryons along a relativistic constituent quark model (RCQM) that had already provided for a reasonable description of the baryon spectra with u, d, and s flavors based on the dynamics of Goldstone-boson exchange (GBE) [5,6]. As we discussed at the 2018 Bled Mini-Workshop the same model has subsequently been extended to reach a unified description of the spectroscopy of all known baryons [7,8]. The investigations of the baryon electromagnetic structures started, of course, with the nucleons, whose form factors are most comprehensively and most accurately measured in experiments. Already in 2000 and the following years it was found that the covariant predictions for the elastic proton and neutron form factors as well as their electric radii and magnetic moments were obtained (without any introduction of additional parameters beyond the already established GBE RCQM) in surprisingly good agreement with phenomenological data [9-11]. We remark that a similarly good performance had then be obtained also with regard to the axial and induced pseudoscalar form factors, GA and GP, of the nucleons as well as the axial charge gA [10,12]. All the predictions for covariant electroweak form factors have been calculated in the framework of point-form relativistic dynamics and thus all symmetry requirements of the Poincare group could be ful- filled. 44 W. Plessas Once the flavor components in the nucleon electromagnetic form factors had been revealed by the analysis of the world data from elastic electron scattering on both the proton and neutron (under the assumption of charge symmetry), the GBE RCQM was also subject to these compellent tests. The model passed them quite satisfactorily [13]. As a result, all aspects of the elastic electromagnetic nucleon structures up to momentum transfers of Q2 ~ 4 GeV2 have been well explained. Of course, such subtle, and still lasting, problems like the differences of proton electric radii from distinct measurements (see, e.g., the values reported by the Particle Data Group [14] and the corresponding references therein) could not be resolved in the framework of a RCQM. Here, we like to add the remark that the probing of the nucleon structure not only in electromagnetic and weak processes but also by strong and gravitational interactions has likewise led to satisfactory results. The covariant predictions of the nNN vertex form factor GnNN, including the nNN coupling constant fnNN, as well as the gravitational form factor A(Q2) all turn out as quite reasonable [15,16]. For a more detailed discussion of these aspects see the review in ref. [17]. The lessons that had been learned from the investigations addressed above were in the first instance: • It is most important to have nucleon/baryon wave functions including all, even small, symmetry components supported by spatial, angular momentum, spin, flavor, and color degrees of freedom. • A fully relativistic framework must be employed such that frame independence is met. • Current conservation must be guaranteed for. In this spirit we have subsequently extended the investigations of the electromagnetic and axial structures to all of the baryons with u, d, and s flavors [1821]. Except for baryon magnetic moments and electric radii, already studied in ref. [11], there are hardly any further experimental data available. However, one can compare with a series of results from lattice quantum chromodynamics (QCD). In particular, such results exist by various groups for the electromagnetic form factors of the A, A, I, E, and the H, see, e.g., refs. [22,15,24,25]. Of course, such comparisons must be taken with care, since the same lattice-QCD calculations may not be entirely reliable, as they are facing already problems in the nucleon sector, especially with the description of the neutron electric form factor in comparison with experimental data, and they still exhibit considerable uncertainties. Additional doubts may be put on previous lattice-QCD calculations of electromagnetic form factors due to opposite-parity contaminations in the lattice data [11]; see also the contribution by Finn M. Stokes in the present proceedings. Some of our results for electromagnetic form factors of singlet, octet, and decuplet baryons have already been published in refs. [13,17,21,27], and we refrain from repeating them here. In refs. [13,27] we have also presented flavor decompositions of the A, I, and A electromagnetic form factors. All of the predictions by the GBE RCQM appear to be quite reasonable, and no striking failures are found for the electromagnetic structures of the nucleon, A, and hyperon ground states. Electromagnetic Form Factors of the Nucleons, the A, and the Hyperons 45 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0 12 3 Q2 [GeV2/c2] 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0 12 3 Q2 [GeV2/c2] Fig. 1. Comparison of the elastic magnetic form factors of the octet r°(u, d, s) and the decuplet Z*° (u, d, s) together with their individual u, d, and s flavor contents as predicted by the GBE RCQM [5] under the assumption of charge symmetry. The data points at Q2 =0.227 GeV2 are due to the lattice-QCD calculations by Boinepalli et al. [15,24]. In order to stress the necessity for refined baryon wave functions for applications beyond spectroscopy, we show here only a comparison of the distinct features of the flavor compositions of form factors of hyperons with the same flavor contents but belonging to different flavor multiplets, i.e. either to the octet 1/3 GUMZ0(Q2)=1/3 GUMZ(Q2) 1/3 GM„z (Q2), (Q2)=-1/3 GMZ(Q2)) 1/3 GSMZ°(Q2)=-1/3 GMz(Q2) Boinepalli: 1/3 GMZ (Q2 mn=306(7)MeV Boinepalli:-1/3 gMz (Q' mn=306(7)MeV Boinepalli:-1/3 gm mn=306(7)MeV Boinepalli: gM (Q2) mn=306(7)MeV gM*0 (Q2) £*0 0(Q)="3GM -1/3 GdMZ*0(Q2)=-1/3 GdMZ*(Q2) -1/30GSMZ* (Q2)=-1/3 GSMZ*(Q2) gM (Q2) Boinepalli: 1/3 GMZ (Q2), ---- 1/3GMZ*"(Q2)=1/3GMZ*(Q2) mn=306(7)MeV Boinepalli:-1/3 gMz*(Q2), mn=306(7)MeV Boinepalli:-1/3 ( mn=306(7)MeV E*0 Boinepalli: GM mn=306(7)MeV Boinepalli:-1/3 GMZ*(Q2), 46 W. Plessas or decuplet. Take, for instance, the octet I0(u, d, s) vs. the decuplet I*0(u, d, s) ground states. While the flavor part of the latter is completely symmetric, the one of the former is mixed-symmetric, like the one of the neutron, say, sitting in the same octet. This has decisive consequences especially for magnetic form factors with regard to both the total results as well as the different flavor contributions. The situation is illustrated in Fig. 1. While the contributions by the u and d flavors are similar in both cases, the s contributions are completely different. They come even with different signs, what is simply a consequence of the distinct flavor symmetries in the pertinent wave functions. Quite similar behaviours as shown in Fig. 1 are found for the octet E(d, s, s) and the decuplet E*(d, s,s), which have again the same flavor contents. These findings simply stress the necessity of having baryon wave functions with accurate flavor components in interplay with the other (spatial, angular momentum, spin, and color) ingredients. From the results of our investigations one may conclude that {QQQ} valence-quark degrees of freedom are essentially sufficient to reproduce the electromagnetic structures of baryons (elastic form factors) at low momentum transfers. Higher Fock components play no or at most a minor role. Explicit n (and maybe other mesonic) contributions will finally have to be included in order to reach a more accurate and a more consistent description, especially in concordance with excited resonance states, e.g., for N —» A electromagnetic transitions. First attempts to simultaneously cover the nucleons (as ground states) and their first few excitations (as true resonant states) are under way along coupledchannels (CC) RCQMs. So far only the bare N and A states coupled to nN and nA channels have been considered [28,29]. One has seen that coupling of bare {QQQ} states to these channels produces pionic effects in the N mass of about 10-15 %. For the form factors, however, the corresponding effects are tentatively found to be smaller [30-32]. It will be a challenging task for future investigations to treat the baryon ground states together with their resonances in CC frameworks both with regard to spectroscopy as well as all kind of form factors and reactions. Acknowledgements The author is very grateful to Bojan Golli, Mitja Rosina, and Simon Sirca for their continuous efforts of organizing every year the Bled Mini-Workshops. These meetings, largely characterized by an informal atmosphere, serve as a valuable institution of exchanging ideas and of mutual learning among an ever growing community of participating colleagues engaged in hadronic physics. In 2019 we have enjoyed the 21st edition thereof, and our best wishes are due for many more such Mini-Workshops to happen in the future. Corresponding efforts should be supported in every respect. Results of the GBE RCQM regarding electromagnetic baryon form factors cited and addressed in this contribution have mainly been obtained in collaboration with Robert Wagenbrunn, Ki-Seok Choi, and Martin Rohrmoser. Electromagnetic Form Factors of the Nucleons, the A, and the Hyperons 47 References 1. G. D. Cates, C. W. de Jager, S. Riordan and B. Wojtsekhowski, Phys. Rev. Lett. 106, 252003 (2011) 2. I. A. Qattan and J. Arrington, Phys. Rev. C 86, 065210 (2012) 3. M. Diehl and P. Kroll, Eur. Phys. J. C 73, 2397 (2013) 4. I. A. Qattan, J. Arrington and A. Alsaad, Phys. 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[Particle Data Group], Phys. Rev. D 98, 030001 (2018) 15. T. Melde, L. Canton, and W. Plessas, Phys. Rev. Lett. 102,132002 (2009) 16. J. P. Day, PhD Thesis, University of Graz (2013) 17. W. Plessas, Int. J. Mod. Phys. A 30,1530013 (2015) 18. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Phys. Rev. C 81, 028201 (2010) 19. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Phys. Rev. D 82, 014007 (2010); ibid. 039901 (2010) 20. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Few-Body Syst. 50, 203 (2011) 21. K.-S. Choi and W. Plessas, Few-Body Syst. 54,1055 (2013) 22. C. Alexandrou, Prog. Part. Nucl. Phys. 67,101 (2012) 23. S. Boinepalli, D. B. Leinweber, A. G. Williams, J. M. Zanotti and J. B. Zhang, Phys. Rev. D 74, 093005 (2006) 24. S. Boinepalli, D. B. Leinweber, P. J. Moran, A. G. Williams, J. M. Zanotti and J. B. Zhang, Phys. Rev. D 80, 054505 (2009) 25. H. W. Lin and K. Orginos, Phys. Rev. D 79, 074507 (2009) 26. F. M. Stokes, W. Kamleh and D. B. Leinweber, Phys. Rev. D 99, 074506 (2019) 27. M. Rohrmoser, K. S. Choi, and W. Plessas, Few-Body Syst. 58, 83 (2017) 28. R. A. Schmidt, L. Canton, W. Schweiger and W. Plessas, J. Phys. Conf. Ser. 738, 012045 (2016) 29. R. A. Schmidt, L. Canton, W. Plessas and W. Schweiger, Few-Body Syst. 58, 34 (2017) 30. B. Pasquini and S. Boffi, Phys. Rev. D 76, 074011 (2007) 31. J. H. Jung, W. Schweiger and E. P. Biernat, Few-Body Syst. 60,13 (2019) 32. W. Plessas and R. A. Schmidt, Few-Body Syst. in print Bled Workshops in Physics Vol. 20, No. 1 p. 48 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Heavy-Quark Exotics Jonathan L. Rosner Enrico Fermi Institute, University of Chicago, 5640 Ellis Avenue, Chicago, IL 60637 Abstract. The heavy quarks c and b stabilize exotic meson (qq q q) and baryon ( q q q q q) states. We discuss work with M. Karliner on molecules containing cc and bb; the first doubly charmed baryon; isospin splittings; S+c = ccd and Qcc = ccs masses; lifetimes; tetraquarks stable under strong and electromagnetic decay; excited Qc states; and P-wave excitation energies. In 1964 M. Gell-Mann [1] and G. Zweig [2] proposed that the known mesons were qq and baryons qqq, with quarks known at the time u ("up"), d ("down"), and s ("strange") having charges (2/3,-1/3,-1/3). Mesons and baryons would then have integral charges. Mesons such as qqqq and baryons such as q q q qq would also have integral charges. Why weren't they seen? They have now been seen, as "molecules" of heavy-quark hadrons or as deeply bound states involving heavy quarks (charm and bottom). An early prediction of exotics was based on duality between s-channel and t-channel processes [3]. In antiproton-proton scattering, qq is dual to qqqq, predicting "exotic" qqqq mesons. Where would they occur? One picture of resonance formation is based on qq annihilation [4]. If p* is the momentum of each colliding particle in their center of mass, the first (meson-meson, meson-baryon) resonance forms for p* < (350,250) MeV. Optical reasoning then leads one to expect the first baryon-antibaryon resonance to form for p* < 200 MeV. The first "baryonium" candidate was actually the pion [5], envisioned as a nucleon-antinucleon bound state. A QCD string picture can distinguish a standard q q meson, a standard baryon, and an exotic meson from one another. If decays occur via quark pair production (breaking of a QCD string), a qqqq meson will either decay to baryon-antibaryon or to an ordinary meson plus an exotic one. It was proposed [3] to search for exotic mesons in the backward direction of a meson-baryon collision. Such exotics may fall apart into meson pairs and may be too broad to show up as distinct resonant peaks. No resonances made of u, d, s have been seen which would correspond to qqqq but not qq (e.g., uuds decaying to K+n+). Similarly, pentaquark states (4qq) made only of u, d, s have not been confirmed. R. Jaffe made an extensive study of qqqq states within the bag model of QCD [6]. Light diquark-antidiquark states could be familiar ones with masses of a GeV or less. The situation changed with heavy quarks c (charm) and b, which act to stabilize exotic configurations. The charmed quark was introduced in 1964 to preserve Heavy-Quark Exotics 49 lepton-quark symmetry [7]. The suppression of higher-order weak corrections led Glashow, Iliopoulos, and Maiani [8] to estimate mc ~ 2 GeV/c2, while Gaillard and Lee (1973) [9] studied the charmed quark's role in gauge theories. Evidence for the charmed quark c appeared in the cc bound state J/^ [10,11]. An abundant charmonium (cc) spectrum is still evolving. Particles with one charmed quark also display a rich spectrum. The large value of mc allows nonrelativistic quantum mechanics to provide some insights. Evidence for a third quark-lepton family began with observation of the t lepton [12]. The quark-lepton analogy then implied the existence of a quark doublet (t [top], b [bottom]), first predicted by Kobayashi and Maskawa [13] to explain CP violation. Evidence for the b quark came from observation in 1977 at Fermilab of the first members of the Y family of spin-1 bb particles produced in protonproton interactions, decaying to |m+m— [14]. Today there is a rich spectroscopy both of bb states and of "B" mesons containing a single b quark. Decays of particles with b quarks are an active field. The top quark, discovered in 1995 at the Fermilab Tevatron [15], has a mass mt ~ 173 GeV so large that it decays too rapidly to have interesting spectroscopy. The first genuine exotic, X(3872), was seen decaying to by the Belle Collaboration in 2003 [16], and confirmed by CDF [17], D0 [18], and BaBar [19]. Its identification as a D0D*0 + c.c. molecule comes from its proximity to D0D*0 threshold: M(X) = (3871.69 ± 0.17) MeV ~ M(D0) + M(D*°) = (3871.68 ± 0.07) MeV. Its decay X —» yJ/^ is seen, implying C(X) = + and some admixture of cc in its wave function. The angular distribution of its decay products implies JPC = 1++ as expected for an S-wave state of D0D*0 + c.c. [20]. C invariance implies the n+n- pair in its decay has negative C, as in a p meson. The large value of M(D(*)+) - M(D(*)0) implies little D(*'± in its wave function. The comparable rates for r(X —» ^J/^) and r(X —» J/^p) are what one would expect for a state with a ccuu admixture. In addition to the X(3872) (a mixture of 23Pi cc and JPC = 1++ ccuu) one expects an orthogonal mixture, typically above 3900 MeV in potential models. The Belle Collaboration saw unexpected structures Zb (10610,10650) in M[n±Y(1S, 2S, 3S)] when studying Y(10865) -> Y(1S,2S,3S)n+n- [21] (Fig. 1). All spectra showed peaks at M(Y(nS)n = 10.61 and 10.65 GeV, within a few MeV of M(B) + M(B*) and M(B*) + M(B*). These look like S-wave molecules of BB*(+c.c.) and B*B*. Fig. 1. Mass spectra M(Y(1S, 2S, 3S)n+) in Y(10865) ^ Y(1S,2S,3S)n+n- [21]. 50 Jonathan L. Rosner Evidence for ccuud configurations has been provided by LHCb [22], who observed bumps in the J/^ p invariant mass in the decay Ab —> K-J/^ p at 4380 and 4450 MeV. (See Fig. 2 for a production mechanism.) Fig. 2. Production mechanisms in Ab decays. Left: A* excitation; right: Pc excitation. The K-J/^ p Dalitz plot (Fig. 3) is populated by many I = 0 K-p states. In an updated result [23], LHCb sees three narrow J/^ resonances at 4311.9, 4440.3, 4457.3 MeV, with widths 9.8, 20.6, 6.4 MeV. The masses are near IcD and IcD* thresholds; if these are molecules, their binding mechanism is unclear. One-pion exchange can't couple to DO; n+n- exchange may favor IcD over DID: the lowest intermediate state is AcD* vs. D*D*. The asymmetric behavior along M(J/^ p) bands indicates interference with opposite-parity amplitude(s). 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 [GeV2] Fig. 3. K-J/^ p Dalitz plot in Ab -> K-J/^ p [23] So far we have discussed QQq q' or QQqqq' states, where Q = heavy, q, q' = light. Can we predict masses of (simpler) QQ'q systems? The SELEX Collaboration at Fermilab [24] claimed states E++(3520) = ccu and E+c(3460) = ccd which were not confirmed by others. Using constituent-quark masses, hyperfine splittings, and estimates of QQ' binding M. Karliner and I [25] predicted the masses in Table 1. In 2017 the LHCb Collaboration found a E+c+ candidate with mass 3621.40 ± 0.78 MeV [26], in accord with our estimate. Other estimates (> 30) had Heavy-Quark Exotics 51 Table 1. Masses of ground-state doubly heavy baryons predicted in Ref. [25] State Quark content M(J = 1/2) M(J = 3/2) —cc ccq 3627±12 3690 ± 12 "bc b[cq] 6914 ± 13 6969 ± 14 "bc b(cq) 6933 ± 12 - "bb bbq 10162 ± 12 10184 ± 12 a spread of at least 100 MeV. The spectra displaying the resonance are shown in Fig. 4. No peak is seen in AcK0n+. We predicted t(E++'+) = (185,53) fs. A AcK-n+ peak is disfavored by the LHCb lifetime cut t > 150 fs. The "++ lifetime was measured by LHCb to be 256+22 ± 14 fs [27]. The mass in the channel was measured to be 3620.6±1.5±0.4±0.3 MeV [28]. The masses of the doubly heavy baryons were calculated with inputs reproducing the light-quark baryons as shown in Table 2. One describes light-quark mesons with quark masses ~ 54 MeV less. M(Ac,b) — M(A) implies mc,b = (1710.5,5043.5) MeV. These masses are sufficient to describe nonstrange baryons with one c or b quark, when taking account of deeper cs or bs binding in baryons with one or two strange quarks and one charm or bottom quark (see Table 3). When demanding the same quark masses for mesons and baryons, one adds 161.5 MeV for a baryon string junction. The fit quality remains the same. A quark pair is more deeply bound when neither is u or d. For example, the binding energy of a cs pair is B(cs) = [3M(DS) + M(Ds)]/4 — ms — mc = —69.9 MeV. If one assumes B(cs)/B(cs) = 1/2 as for single-gluon exchange then B(cs) = —35 MeV. A similar calculation gives B(bs) = —41.8 MeV. One must rescale hyperfine interactions when neither quark is u or d. We take a cue from M(DS) — M(Ds) ~ M(D*) — M(D). 52 Jonathan L. Rosner Table 2. Masses of light-quark baryons predicted with mu = md = mq = 363 MeV, ms = 538 MeV, and hyperfine interaction term a/(mq )2 = 50 MeV State (mass in MeV) Spin Expression for mass Predicted mass (MeV) N(939) 1/2 3mq — 3a/(mq)2 939 A(1232) 3/2 3mq + 3a/(mq)2 1239 A(1116) 1/2 2mq + ms — 3a/(mq)2 1114 1(1193) 1/2 2mq + ms + a/(mq )2 — 4a/mq ms 1179 1(1385) 3/2 2mq + ms + a/(mq )2 + 2a/mq ms 1381 E(1318) 1/2 2ms + mq + a/(ms)2 — 4a/mqms 1327 E(1530) 3/2 2ms + mq + a/(ms)2 + 2a/mqms 1529 Q(1672) 3/2 3ms + 3a/(ms)2 1682 Table 3. Predicted masses of baryons containing one charm or bottom quark. Charmed baryons Bottom baryons State (M Spin Predicted State (M Spin Predicted in MeV) M (MeV) in MeV) M (MeV) Ac (2286.5) 1/2 Input Ab (5619.5) 1/2 Input Ic (2453.4) 1/2 2444.0 Ib(5814.3) 1/2 5805.1 Z* (2518.1) 3/2 2507.7 Ib (5833.8) 3/2 5826.7 Ec(2469.3) 1/2 2475.3 Eb (5792.7) 1/2 5801.5 EC (2575.8) 1/2 2565.4 Eb (—) 1/2 5921.3 E* (2645.9) 3/2 2628.6 Eb (5949.7) 3/2 5944.1 Qc (2695.2) 1/2 2692.1 Qb (6046.4) 1/2 6042.8 QC (2765.9) 3/2 2762.8 Qb(—) 3/2 6066.7 Charm-anticharm binding gives B(cc) = [3M(J/^) + M(nc)]/4 — 2m,m = -258 MeV, so B(cc) = —129 MeV. Similar calculations give B(bb) = —281.4 MeV and B (bc) = —167.8±3.0 MeV, where the error reflects uncertainty in the BC mass. One now can calculate the doubly heavy ground state baryon masses in Table 1. A study of isospin splittings in doubly heavy baryons [29] was motivated by the large (60 MeV!) splitting between E+c(3460) and E+c+(3520) claimed by SELEX [24]. It was found that M(E+C+) — M(E+C) = 2.17 ±0.11 MeV if separate quark masses are used for light mesons and baryons, or 1.41±0.12 MeV if universal masses are used. Contributions to mass differences are shown in Table 4. For details of these calculations and well-obeyed fits to known isosplittings in light-quark and charmed baryons see Ref. [30]. In Table 5 we compare various predictions for M(E+C+) — M(E+C). A spread of values is obtained, but nearly all are at most a few MeV. Some authors still entertain the possibility that the SELEX result is correct, with physics beyond standard model. This could be put to rest if LHCb sees a E+C at or slightly Heavy-Quark Exotics 53 Table 4. Contributions to isospin splittings (HF=hyperfine interaction) if (separate, universal) quark masses are used. Param- Quantity Contribution in MeV to eter M(p) - M(n) M(S++)- M(S+) A mu - md -2.48,-2.67 -2.48,-2.67 a Coulomb 1.02, 0.94 4.07, 3.77 b Strong HF 0.67, 0.88 -0.29,-0.33 c EM HF -0.51,-0.43 0.86, 0.64 Total -1.29,-1.29 2.17,1.41 Table 5. Comparison of predictions for isospin splittings of Ecc states. Author(s) Reference M(S++)- M(S+) (MeV) Karliner + PR D 96,033004 (2017) 1.41 ± 0.12+0.76 Itoh + PR D 61, 057502 (2000) 4.7 Brodsky + PL B 698, 251 (2011) 1.5 ± 2.7 Hwang + PR D 78, 073013 (2008) 2.3 ± 1.7 Borsanyi + Science 347,1452 (2015) 2.16 ± 0.11 ± 0.17 Lichtenberg PR D 16, 231 (1977) 4.7 Tiwari + PR D 31, 642 (1985) 1.11 Shah + Rai EPJC 77,129 (2017) -9 below 3620 MeV (an observation made more difficult by its expected short lifetime). The "spectator" process c —» sW* , where W* goes to (e+ve, M-+ , 3 colors of ud), dominates E+c+ decay. One can emulate kinematic suppression with xcc = [M(Ec/M(Ecc)]2: r(E++) = 10G2mn+r+)5 F(xcc) , F(x) = 1 - 8x + 8x3 - x4 + 12 ln(1/x), implying t(E++) = 188 fs. An additional "exchange" process cd —» su contributes to E+c = ccd decay. The "spectator" partial width is Fs = h/t(E+c+) = h/(256 fs) = 2.57 x 10-12 GeV, while the "exchange" partial width is Fe = 2[h/t(E0) -h/t(E+)] = 5.64 x 10-12 GeV. Here we have used t(E0) = 154.5 ± 1.7 ± 1.6 ±1.0 fs; t(E+) = 458.8 ± 3.6 ± 2.9±3.1 fs [31]. Adding the two, Fs + Fe = 8.21 x 10-12 GeV implies t(E+c) = 80 fs, our updated prediction. One can predict the mass of Hcc = ccs using the methods just described. The strange quark is about 175 MeV heavier than nonstrange but more deeply bound to the cc diquark than the nonstrange quark. We compare the predictions for ccq and ccs in Table 6. 54 Jonathan L. Rosner Table 6. Comparison of predictions for ccq and ccs ground-state baryon masses. -cc = ccq Qcc = ccs Contribution Value (MeV) Contribution Value (MeV) 2mc + mq 3789.0 2mc + ms 3959.0 cc binding —129.0 cc binding —129.0 acc/(mc)2 14.2 acc/(mc)2 14.2 —4a/mq mc —42.4 —4a '/ms mc —42.4 Total 3626.8 ± 12 Subtotal 3801.8 ± 12 The additional binding of s to cc is -109.4 ± 10.5 MeV, giving M(ncc) = 3692 ± 16 MeV, M(n*c) = 3756 ± 16 MeV, With universal quark masses and a 161.5 MeV "string junction" term for baryons one predicts M(Hcc) ~ 40 MeV higher. M. Karliner and I investigated QQ'ud systems [32], where Q, Q' = c or b. We found ccud unbound; it could decay to DD* or DDy. The lowest-lying bcud state was near BDy threshold and could be bound. We predicted M(bbud) = 10,389 ± 12 MeV, 215 MeV below B-B*0 threshold and 170 MeV below B-B0y threshold. Regarding bb as a color-3* diquark (transforming under QCD as an antiquark), fermi statistics required its spin to be 1. The lightest qq' state (q, q' = u, d) is a color-3 ud state with isospin zero; fermi statistics require its spin to be zero. The mass prediction then relies on accounting for constituent-quark masses, hyperfine interactions, and binding effects (Table 7). Table 7. Contributions (in MeV) to mass of lightest QQ' q q' tetraquark. ccud, JP = 1 + bcud, JP = 0+ bbud, JP = 1 + Contribution Value Contribution Value Contribution Value 2mb 2mq cc hyperfine —3a/(mq)2 cc binding Total 3421.0 726.0 14.2 —150.0 —129.0 3882±12 mb + mc 2mq bc hyperfine —3a/(mq)2 bc binding Total 6754.0 726.0 —25.5 —150.0 —170.8 7134±13 2mb 2mq bb hyperfine —3a/(mq)2 bb binding Total 10087.0 726.0 7.8 —150.0 —281.4 10389±12 Spin zero is allowed for the bcud state, taking advantage of the attractive bc hyperfine interaction. Since M(ccud) > M(D0) + M(D + ) = 3734 MeV, it can decay to D0D+y (decay to D0D+ is forbidden). We cannot tell whether M(bcud) is less than M(D0) + M(B0) = 7144 MeV. The estimated lifetime of the bbud state is 367 fs. The LHCb Collaboration has presented evidence for five narrow nc states decaying to E+K- [33]. (Already known were the ground css states: Hc(2695,1 /2+) Heavy-Quark Exotics 55 and nc(2766,3/2+) [4].) Marek Karliner and I [35] identified the narrow states as five P-wave excitations, with an alternative assignment of the two highest-mass states as positive-parity radial excitations of the ground states. In that case two JP = 1/2— states would remain to be seen, one around 2904 MeV decaying to Hcy and/or Hcn0, and the other around 2978 MeV decaying to E+K— in an S-wave. What does it cost to excite a hadron from S-wave to P-wave [36]? Defining a residual energy AER = AEPS-B12, where B12 is the binding energies of constituents, we found a good fit with AEr = (417.37 — 0.2141|12) MeV, where |12 is the reduced mass. The prospects for exotic mesons and baryons (beyond q q and qqq) are bright. 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Zweig, CERN-TH-401; Developments in the Quark Theory of Hadrons, Volume 1, edited by D. Lichtenberg and S. Rosen, p. 22. 3. J. L. Rosner, Phys. Rev. Lett. 21, 950 (1968). 4. J. L. Rosner, Phys. Rev. D 6, 2717 (1972). 5. E. Fermi and C. N. Yang, Phys. Rev. 76,1739 (1949). 6. R. L. Jaffe, Phys. Rev. D 15, 267, 281 (1977); Phys. Rev. D 17,1444 (1978). 7. J. D. Bjorken and S. L. Glashow, Phys. Lett. 11,255 (1964); Z. Maki and Y. Ohnuki, Prog. Theor. Phys. 32,144 (1964); Y. Hara, Phys. Rev. 134, B701 (1964); D. Amati, H. Bacry, J. Nuyts, and J. Prentki, Nuovo Cim. 34,1732 (1964); Phys. Lett. 11,190 (1964). 8. S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2,1285 (1970). 9. M. K. Gaillard and B. W. Lee, Phys. Rev. D 10, 897 (1973). 10. J. J. Aubert et al. [E598 Collaboration], Phys. Rev. Lett. 33,1404 (1974). 11. J. E. Augustin et al. [SLAC-SP-017 Collaboration], Phys. Rev. Lett. 33,1406 (1974). 12. M. L. Perl et al, Phys. Rev. Lett. 35,1489 (1975). 13. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). 14. S. W. Herb et al., Phys. Rev. Lett. 39, 252 (1977); W. R. Innes et al., Phys. Rev. Lett. 39, 1240 (1977); Erratum: [Phys. Rev. Lett. 39,1640 (1977)]. 15. F. Abe et al. [CDF Collaboration], Phys. Rev. Lett. 74, 2626 (1995); S. Abachi et al. [D0 Collaboration], Phys. Rev. Lett. 74, 2632 (1995). 16. S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. 91, 262001 (2003). 17. D. Acosta et al. [CDF Collaboration], Phys. Rev. Lett. 93, 072001 (2004). 18. V. M. Abazov et al. [D0 Collaboration], Phys. Rev. Lett. 93,162002 (2004). 19. B. Aubert et al. [BaBar Collaboration], Phys. Rev. D 71, 071103 (2005). 56 Jonathan L. Rosner 20. K. Abe et al. [Belle Collaboration], contributed to 22nd International Symposium on Lepton-Photon Conference, arXiv:hep-ex/0505038. 21. A. Bondar et al. [Belle Collaboration], Phys. Rev. Lett. 108,122001 (2012). 22. R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 115, 072001 (2015). 23. R. Aaij et al. 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Lett. 119, 202002 (2017). 33. R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 118,182001 (2017). 34. M. Tanabashi et al. [Particle Data Group], Phys. Rev. D 98, 030001 (2018). 35. M. Karliner and J. L. Rosner, Phys. Rev. D 95,114012 (2017). 36. M. Karliner and J. L. Rosner, Phys. Rev. D 98, 074026 (2018). 37. M. Karliner and J. L. Rosner, Nature 551, 89 (2017). Bled Workshops in Physics Vol. 20, No. 1 p. 57 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Effect of intermediate resonances in the quark-photon vertex Helios Sanchis-Alepuz University of Graz, A-8010 Graz, Austria Abstract. We summarise the main results of the paper [1] in which the effects on the quark-photon vertex of intermediate hadronic resonances in the quark-antiquark interaction kernel are studied. This is a first step in the long road of including non-valence contributions to hadron properties in the Bethe-Salpeter approach. 1 Introduction. Non-valence effects A detailed and quantitatively reliable description of hadron structure at low and medium energy is a decade-old problem that is, curiously, becoming more and more relevant. Its most obvious goal is to characterize hadrons: we wish to be able to calculate their masses, radii, magnetic moments, axial charges, etc. Moreover, we expect to gain understanding of QCD as the theory of the strong interactions: for example, if we are able to interpret measurements of form factors, this gives us a handle on the underlying QCD mechanisms forming hadrons. But also, current experimental facilities searching for beyond Standard model (BSM) physics are mainly hadronic machines; therefore, in order to extract new physics from the measurements one must convolute possible effective BSM operators with hadronic states and then calculate the measurable effect. Example of these are the extraction of CKM elements from processes involving heavy mesons or attempts to measure quark electric dipole moments (EDM) from neutron EDMs, etc. The study of QCD and, in particular, its non-perturbative aspects phenomena can be approached using Dyson-Schwinger (DSE) and Bethe-Salpeter (BSE) equations. DSEs are non-linear integral equations describing the Green's functions (GFs) of the theory and BSEs are linear integral equations for bound states. Even though a full non-perturbative treatment of the quark-photon vertex would require to solve the corresponding DSE, if one is interested in QCD effects only, these can be studied with equations simpler than DSEs, namely inhomogeneous BSEs. The combination of DSEs and (homeogeneous and inhomogeneous) BSEs has been extensively and successfully used to study hadron phenomenology [2]. The complexity of non-perturbative calculations entails that nearly always some sort of approximation or simplification is necessary. In the context of DSEs and BSEs, it is necessary to truncate the infinite system of coupled DSEs that describe the theory and the infinite number of interaction terms in a BSE, as described below. Truncations of ever increasing sophistication that perform well 58 Helios Sanchis-Alepuz phenomenologically have been developed over the years (see e.g. [3,4,2,5] and references therein). However, the rainbow-ladder (RL) truncation of the BSE interaction kernel is the most sophisticated truncation used so far in the calculation of hadron form factors. Here, the quark-antiquark interaction kernel is simplified to a single-gluon exchange, augmented by an effective interaction, meant to include all other effects. Even though it performs remarkably well on the calculation of hadron form factors for spacelike momentum region, the trend in all cases is that the RL truncation is insufficient to describe the behaviour of form factors at low photon momentum. The reason for that is usually attributed to RL calculations lacking so-called meson-cloud effects on form factors, which stem from the photon coupling to non-valence quarks inside the hadron (sea quarks). Meson-cloud effects are a manifestation of the presence of non-valence degrees of freedom inside a hadron, which which an external field can and does interact. In the BSE approach these can only appear in the BSE interaction kernel. An example of how this could happen is shown in Fig. 1. In addition to providing meson-cloud effects, non-valence terms have other crucial implications, such as enabling virtual transitions that account for the non-vanishing decay width of some states or providing a source for the strangeness content of nucleons. We want to focus here on the former, since this suffices as we will see to generate the qualitatively correct analytic structure for a resonant solution of the BSE. Fig. 1. (Upper panel) Schematic representation of a baryon (B) BSE. The term Kvaience represents an interaction kernel with only valence quark lines. The last term represents, via the quark-antiquark scattering matrix T, non-valence contributions to the BSE kernel. Lines with blobs are fully-dressed quark propagators. (Lower panel) The first two diagrams show the coupling of an external current via current insertions (crosses) in a LQCD calculation (adapted from [6]), with the first diagram representing the coupling to valence quarks (connected contributions) and the second diagram the coupling to a non-valence quark (disconnected contribution). To the right we show two possibles ways how, in a BSE calculation of FFs, an external field would couple to non-valence quarks. In this work we study a simplification of such a scenario and its effects on the quark-photon interaction vertex. The quark-photon vertex describes the interaction of quarks with photons in quantum field theory. It is, therefore, a crucial ingredient in the study of the electromagnetic interaction of hadrons. Those couplings are described by the spacelike and timelike form factors of hadrons. Effect of intermediate resonances in the quark-photon vertex 59 It is well known that the strong interactions among quarks generates a structure of the quark-photon vertex much richer than its tree-level component y^. In particular, for timelike photon momentum, the quark-photon vertex must reflect the full excitation spectrum of quantum chromodynamics (QCD) in the vector-meson channel, a fact which is at the heart of the phenomenological success of vector-meson dominance models. The details of such a rich structure of the vertex are, however, not precisely known since they are generated by non-perturbative QCD effects. We present here the results of a study [1] in which we used an extension of the RL truncation which encodes, to some extent, the above-mentioned non-valence quark effects on the BSE interaction kernel. The truncation studied herein was put forward in [7,8] and keeps the resonant contributions of non-valence terms only, describing them in terms of explicit pionic degrees of freedom. In particular, the new kernel includes a virtual decay channel of e.g. a vector meson into two pions. We have shown that this kernel generates the correct physical picture of the quark-photon vertex on the timelike momentum side, as mentioned above. Moreover, it is reasonable to expect that a calculation of form factors with the kernel used in this work must, to some extent, alleviate the problem of missing meson-cloud effects. 2 Non-valence effects on the quark-photon vertex The details of this calculation are omitted here and the reader is referred instead to the full publication [1]. Moreover, we focus here on the changes on the timelike structure of the vertex, since it is here that the connection with the resonant structure of QCD becomes clear. We begin by showing in Fig. 2 the results of the quark-photon vertex using the RL truncation only. Specifically, in what follows we plot the twelve dressing functions describing a non-perturbative quark-photon vertex, as a function of the photon momentum Q. Note that the qualitative features of the solution are the same for any truncation not including non-valence contributions. As said, we show here the timelike Q2 <0 only. In this region, the vertex is sensitive to the quark-antiquark bound states with the quantum numbers of the photon JPC = 1 , which include the rho meson and its excitations. Because for the RL truncation all hadrons are bound states with no width, this is manifested here in Fig. 2 by the appearance of poles of the vertex dressing functions for the values of Q2 corresponding to the bound-state masses. For a realistic interaction kernel, however, those solutions should be resonances and the pole occurs for complex values of Q2 corresponding to the pole mass Q2 = —M2 + iMT, with M and r the Breit-Wigner mass and width of the resonance, respectively. That is, the analytic structure of the quark-photon vertex should feature isolated poles. Additionally, the possible decay modes in a given Green's function manifest themselves as the typical multiparticle branch cut, starting at the particle production threshold. We exemplify this behaviour in Fig. 3 which shows four dressings of the quark-photon vertex, this time with a kernel which includes non-valence degrees 60 Helios Sanchis-Alepuz 1.5 0.5 -0.5 -1 -1.5 A1 A1 -0.45-0.3-0.15 0 Q2 [GeV2] 12 10 0.45 -0.3 -0.15 0 Q2 [GeV2] 12 10 0.45 -0.3 -0.15 0 Q2 [GeV2] Fig. 2. Dressing functions for the non-transverse (Ai) and transverse (hi) components of the quark-photon vertex in the Q2 <0 region for the RL truncation (solid lines) and with the addition of a t-channel pion exchange (dashed lines). See [1] for further details. The vertical solid and dashed lines indicate the position of the rho mass (—mp), as obtained from the solution of an homogeneous BSE with the same truncated kernels. 1 8 8 6 6 0 4 4 2 2 0 0 2 2 of freedom in the form of the exchange of two pions in the u— and s—channels (see [1]). In this case, the two intermediate pions go on-shell when Q2 = —4m^ and thus represent, in particular, the p —» nn decay channel. The dressings of the transverse components should feature a branch cut starting at the real and negative branch point Q2 = —4m^. This is seen in Fig. 3 as a discontinuity in the imaginary part of the dressing functions. That is, the BSE kernel studied in [1] is capable of partially describing the resonance character of the rho meson as a solution of the homogeneous BSE. In the present context, this simply means that the rho-meson bound-state pole of the transverse dressings of the quark-photon vertex, appearing for real Q2 values in Fig. 2, moves to the second Riemann sheet of the Riemann surface that is now the domain of the dressing functions. Effect of intermediate resonances in the quark-photon vertex 61 Fig. 3. Real and imaginary parts of four of the transverse dressing functions of the quarkphoton vertex in a region of the complex Q2-plane with Re(Q2) < 0 with a truncation including non-valence terms (for details see [1]. Even though not clearly visible in the plots, the branch cut in the imaginary parts begins at Q2 = —4m.n. 3 Summary In the work [1] we have studied the non-perturbative structure of the quarkphoton interaction vertex in the spacelike photon momentum region Q2 >0 and in a region of the complex Q2-plane with Re(Q2) < 0, for three different truncations of the inhomogeneous BSE that describes it. To the simple RL truncation we have added quark-pion interactions both as a t-channel pion exchange among quark and antiquark as well as s- and u-channel pion-emission channels. By using explicit pionic degress of freedom in addition to quarks and gluons, we aim at partially describing unquenching effects. We have seen how the effect of those intermediate particles is to drastically change the analytic structure of the quark-photon vertex. Whilst for the RL truncation, as well as with the inclusion of a t-channel pion exchange, the vertex only has poles for real and negative values of the photon momentum Q2, upon inclusion of s- and u-channel pion kernels a multiparticle branch cut starting at 62 Helios Sanchis-Alepuz Q2 = —appears and the poles move away of the real axis into the complex plane. Our results for the analytic structure of the vertex are certainly closer to the expected physical picture and, hence, constitute a step forward towards the calculation of timelike hadron form factors in the BSE formalism. 4 Acknowledgments I would like to thank the organisers and, in particular, Willibald Plessas and Mitja Rosina for the kind invitation and for supporting my participation in the Workshop. This work was supported by the project P29216-N36 and the Doctoral Program W1203-N16 "Hadrons in Vacuum, Nuclei and Stars", both from the Austrian Science Fund, FWF. References 1. A. S. Miramontes and H. Sanchis-Alepuz, Eur. Phys. J. A 55 (2019) no.10, 170 doi:10.1140/epja/i2019-12847-6 [arXiv:1906.06227 [hep-ph]]. 2. G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer and C. S. Fischer, Prog. Part. Nucl. Phys. 91 (2016) 1 doi:10.1016/j.ppnp.2016.07.001 [arXiv:1606.09602 [hep-ph]]. 3. H. Sanchis-Alepuz, C. S. Fischer and S. Kubrak, Phys. Lett. B 733 (2014) 151 doi:10.1016/j.physletb.2014.04.031 [arXiv:1401.3183 [hep-ph]]. 4. R. Williams, C. S. Fischer and W. Heupel, Phys. Rev. D 93 (2016) no.3, 034026 doi:10.1103/PhysRevD.93.034026 [arXiv:1512.00455 [hep-ph]]. 5. S. x. Qin, C. D. Roberts and S. M. Schmidt, Few Body Syst. 60 (2019) no.2, 26 doi:10.1007/s00601-019-1488-x [arXiv:1902.00026 [nucl-th]]. 6. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou and A. Vaquero Aviles-Casco, Phys. Rev. D 100 (2019) no.1, 014509 doi:10.1103/PhysRevD.100.014509 [arXiv:1812.10311 [hep-lat]]. 7. C. S. Fischer, D. Nickel and J. Wambach, Phys. Rev. D 76 (2007) 094009 doi:10.1103/PhysRevD.76.094009 [arXiv:0705.4407 [hep-ph]]. 8. C. S. Fischer, D. Nickel and R. Williams, Eur. Phys. J. C 60 (2009) 47 doi:10.1140/epjc/s10052-008-0821-1 [arXiv:0807.3486 [hep-ph]]. Bled Workshops in Physics Vol. 20, No. 1 p. 63 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Partial Wave Analysis of Pion Photoproduction Data with Fixed-t Analyticity Imposed* J. Stahova'b, H. Osmanovica, M. Hadzimehmedovica, R. Omerovica a University of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina b European University Kallos Tuzla, Marsala Tita 2A - 2B, Tuzla, Bosnia and Herzegovina Abstract. We present results of an analytically constrained partial wave analysis of n° photoproduction data. As an input we used the data on p(y,rt°)p and n(y,rt°)n reactions from threshold up to W = 1.95GeV. 1 Introduction In Ref. [1] we have developed a method to impose analyticity of invariant amplitudes in Mandelstam variables s and t on partial wave solution in an iterative procedure. The method consists of two separated analyses, the fixed-t amplitude analysis (Ft AA) and the single-energy partial wave analysis (SE PWA) coupled in such a way that the results from one analysis are used as a constraint in another one. We have applied this method to the n photoproduction p(y ,n)p. It has been shown that iterative procedure converges rapidly. Recently, with minimal changes in computer code, the method was applied to n° photoproduction reaction p(y,n°)p [2]. Natural extension of our method, applied to pion photoproduction processes, is to analyze all pion photoproduction processes simultaneously, taking into account more complicated isospin structure of invariant amplitudes and corresponding partial waves (multipoles) (work in progress). As a first step in this direction, in this article we present results of SE PWA using experimental data from two n° photoproduction reactions (p(y,n°)p, n(y,n°)n). Details about the method and formalism are given in references [1], [2]. 2 Input data We used the data on the p(y,n°)p from several collaborations: A2@MAMI, CBELSA/TAPS, DAPHNE/MAMI and GRAAL. The data on the n(y,n°)n are rather old and incomplete. This part of our input will be updated in an ongoing analysis. Starting from experimental data, input for SE PWA and Ft AA have been prepared using the spline smoothing method [3] as described in references [1], [2]. * Talk presented by J. Stahov 64 J. Stahov, H. Osmanovic, M. Hadzimehmedovic, R. Omerovic Table 1. Experimental data for (p(y,n0)p, n(y,n0)n reactions used in our SE PWA. YP —> n0 P Obs N W[MeV ] Ne Reference Oo 5240 1075 —1541 262 A2@MAMI(2013) [4] 3930 1132 —1895 246 A2@MAMI(2015) [5] 528 1074 —1215 54 A2@MAMI(2013) [4] I 357 1150 —1310 21 A2@MAMI(2001) [6] 471 1383 —1922 31 GRAAL(2005) [7] T 469 1295 —1895 34 A2@MAMI(2016) [8] 157 1462 —1620 8 CBELSA/TAPS(2014) [9] Too 4500 1074 —1291 250 A2@MAMI(2015) [10] P 157 1462 —1620 8 CBELSA/TAPS(2014) [9] Eo0 139 1201 —1537 24 DAPHNE/MAMI(2001) [11] E 88 1481 —1951 5 CBELSA/TAPS(2014) [12] 480 1129 —1878 40 A2@MAMI(2015) [13] F 469 1295 —1895 34 A2@MAMI(2016) [8] Fo0 4500 1074 —1291 250 A2@MAMI(2015) [10] G 3 1232 1 DAPHNE/MAMI(2005) [14] 318 1430 —1727 19 CBELSA/TAPS(2012) [15] H 157 1462 —1620 8 CBELSA/TAPS(2014) [9] yu —> n0 u Obs N W[MeV ] Ne Reference 00 42 35 42 29 1203 — 1517 1323 — 1535 1318 — 1604 1611 — 1869 17 18 17 3 (1977) [16] (1972) [17] (1973) [18] (1967) [19] I 216 1484 — 1912 25 (2009) [20] 3 Results In our SE PWA we fitted multipoles up to Lmax = 5 (40 multipoles). A minimization procedure ( 80 real parameters) was started at initial values which are randomly distributed in a 30 % range around the starting solution MAID 2007 [21]. The Ft AA was performed at 20 equidistant t-values in the range — 1.00GeV2 < t < —0.09GeV2. Resulting multipoles up to L = 2 are shown in Figs. 1 and 2. Our SE solutions are poorly determined at energies W < 1.2GeV and W > 1.7GeV. This is due to the lack of the experimental data. As can be seen from Table 1, in energy range 1.2GeV < W < 1.7GeV we use as much as eight observables, fitting maximally five of them in the same time. At energies W > 1.7GeV the number of observables is much smaller. Situation is even worse below 1.2 GeV where only two observables ( o0,I ), both from p(y,n0)p, were used in our analysis. Partial Wave Analysis of Pion Photoproduction Data ... 65 W [GeV] W [GeV] Fig. 1. (Color online) Reaction p(y,n0)p. Real and imaginary parts of the S-, P - and D-multipoles obtained with starting solution[21] (black line). Multipoles are in mfm 4 Conclusions We applied iterative procedure with the fixed-t analyticity constraints to partial wave analysis of n0 photoproduction experimental data. For both reactions, p(Y,n0)p and n(y,n0)n, we obtained multipoles up to Lmax = 5. Improving the quality of SE PWA solutions in our method requires update of the data base in a way that both, the number of observables and the quality of the data, are increased. 66 J. Stahov, H. Osmanovic, M. Hadzimehmedovic, R. Omerovic Fig. 2. (Color online) Reaction n(y,n0)n. Real and imaginary parts of the S-, P - and D-multipoles obtained with starting solution [21](black line). Multipoles are in mfm References 1. H. Osmanovic, M. Hadzimehmedovic, R. Omerovic, J. Stahov, V. Kashevarov, K. Nikonov, M. Ostrick, L. Tiator, and A. Svarc, Phys. Rev. C 97, 015207 (2018). 2. H. Osmanovic, M. Hadzimehmedovic, R. Omerovic, J. Stahov, M. Gorchtein, V. Kashevarov, K. Nikonov, M. Ostrick, L. Tiator, and A. Svarc, arXiv:1908.05167 (2019). 3. C. de Boor, A Practical Guide to Splines, Springer-Verlag, Heidelberg, 1978, revised 2001. 4. D. Hornidge et al. [A2 and CB-TAPS Collaborations], Phys. Rev. Lett. 111, no. 6, 062004 (2013). 5. P. Adlarson et al. [A2 Collaboration at MAMI], Phys. Rev. C 92, 024617 (2015). Partial Wave Analysis of Pion Photoproduction Data 67 6. R. Leukel, PhD thesis (2001) Mainz University. 7. O. Bartalini at. al. Eur. Phys. J. A 26, 399 (2005). 8. J. R. M. Annand et al. [A2 Collaboration at MAMI] Phys. Rev. C 93, 055209 (2016). 9. J. Hartmann et al. [CBELSA/TAPS Collaboration] Phys. Rev. Lett. 113, 062001 (2014). 10. P. Otte, PhD thesis (2015) Mainz University. 11. I. Preobrajenski, PhD thesis (2001), Mainz University. 12. M. Gottschall et al. [CBELSA/TAPS Collaboration] Phys. Rev. Lett. 112,012003 (2014). 13. J. Linturi, PhD thesis (2015) Mainz University. 14. J. Ahrens et al. Eur. Phys. J. A 26,135 (2005). 15. A. Thiel et al. [CBELSA/TAPS Collaboration] Phys. Rev. Lett. 109,102001 (2012). 16. A. Ando, Physik Daten, Physics Data (Fach-Informationszentrum), Karlsruhe, (1977). 17. C. Bacci et al, Phys. Lett. C 39, 559 (1972). 18. Y. Hemmi et al., Nucl. Phys. B 55, 333 (1973). 19. Klinesmith, PhD Thesis (1967) see GWU. 20. R. Di Salvo et al., Eur. Phys. J. A 42,151 (2009). 21. D. Drechsel, S. S. Kamalov and L. Tiator, Eur. Phys. J. A 34 (2007) 69; and https://maid.kph.uni-mainz.de/. Bled Workshops in Physics Vol. 20, No. 1 p. 68 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Structure and transitions of nucleon excitations from lattice QCD* Finn M. Stokesa'b, Waseem Kamleha, Derek B. Leinwebera aSpecial Research Centre for the Subatomic Structure of Matter, Department of Physics, University of Adelaide, South Australia 5005, Australia bJülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich D-52425, Germany Abstract. The recently-introduced Parity Expanded Variational Analysis (PEVA) technique allows for the isolation of baryon eigenstates on the lattice at finite momentum free from opposite-parity contamination. We find that this technique introduces a statistically significant correction in extractions of the electromagnetic form factors of the ground state nucleon. It also allows first extractions of the elastic and transition form factors of nucleon excitations on the lattice. We present the electromagnetic elastic form factors and helicity amplitudes of two odd-parity excitations of the nucleon. These results provide valuable insight into the structure of these states, and allow for a connection to be made to quarkmodel states in this energy region. 1 Introduction In lattice QCD, instead of the unstable finite-width resonances of nature, we observe a tower of stable excitations. These eigenstates are associated with the physical resonances in a non-trivial manner. Understanding the structure of the states observed in Lattice QCD will enable predictions of the infinite-volume observables of nature via effective field theory techniques [1,2] or an extension of the Lellouch-Luscher formalism [3,4]. Investigating the structure of excited states in lattice QCD is recognised as an important frontier in the field. Progress has already been made in the meson sector [5,6]. Here we tackle the more challenging problem of calculating such quantities in the baryon sector. By using local three-quark operators on the lattice, both the CSSM [7,8] and the Hadron Spectrum Collaboration (HSC) [9,10] observe two low-lying odd-parity states in the resonance regimes of the N*(1535) and N*(1650). In the following we summarise our recent results on the elastic form factors of the ground state nucleon, these two odd-parity states, and the lowest-lying even-parity state accessible through the same operators [11,12]. In addition, we present preliminary results on the transition form factors for the two odd-parity states. These results were made possible through the development of the PEVA technique [13]. * Talk presented by Finn M. Stokes Structure and transitions of nucleon excitations from lattice QCD 69 2 Parity Expanded Variational Analysis (PEVA) The process of extracting elastic from factors of baryonic excited states via the PEVA technique is presented in full in Ref [11]. We provide here a brief summary of this process and the generalisations required to handle transition matrix elements. We begin with a basis of n conventional spin-1/2 operators (xiMl that couple to the states of interest. Adopting the Pauli representation, we introduce the PEVA projector r±p = 1 (I + y4) (I ± iy5ykp k) [13], and construct a set of basis operators X±p i(x) = r±p xi (x), X±p i' (x) = ±r±p y5 Xi(x). We then seek an optimised set of operators (x) that each couple strongly to a single energy eigenstate a. These optimised operators are constructed as linear combinations of the basis operators by solving a generalised eigenvalue problem as detailed in Ref. [13]. We can then construct the eigenstate-projected two-point correlation function G (p; t; a) = Tr ^ e-ipx (D\ (x) (0) , and the three point correlation functions g± (jCi; pp; t2 ,ti; a^ p) = ^ e-ipei(p(n|^±p,(x2) jCi(xi) *+p(0)|n>, xi ,X2 where jCI(x) is the O(a)-improved [14] conserved vector current jCI(x) used in Ref. [15], inserted with a three-momentum transfer q = p' — p. For the elastic case, this choice of current gives the matrix element (a;p';sj^o) |a;p;s> - V e^v u-(p >') (v F (Q2) ^^^ma1 f2 - wom+m^ (F;(Q2)+f2(Q2»- 3 Ground state nucleon We study the extraction of the elastic form factors of the ground state nucleon in detail in Ref. [11]. This analysis is performed on the PACS-CS (2 + 1)-flavour full-QCD ensembles [17], made available through the ILDG [18]. In the paper we demonstrate the efficacy of variational analysis techniques in general, and PEVA specifically, at controlling excited-state contaminations in the electric form factor. Both the PEVA and conventional variational analysis show clear and clean plateaus, supporting previous work demonstrating the utility of variational analysis in calculating baryon matrix elements [19,20]. 2 =L S Is - (J Ï5 II Î up (PEVA) Ï dp (PEVA) 5 5 Up (Conv.) dp (Conv.) 21 22 23 24 25 t/a \2 26 27 28 (a) Plateaus at Q2 = 0.166(4) CQ O 0.8 0.7 0.6 0.5 t Î CQ (J 0.4 u Up dp 0.0 0.2 0.4 Q2 / GeV2 rr 0.6 (b) Ratios of conventional plateaus to PEVA Fig. 1. Comparison of conventional and PEVA extractions of G M (Q2) for the ground-state nucleon at mn = 156 MeV. Results are contributions for single quarks of unit charge from the doubly represented quark sector (up) and the singly represented quark sector (dp). 0 2 Here we focus on the particular case of the magnetic form factor, where we found evidence that the conventional analysis is contaminated by opposite-parity states. In Fig. 1a we plot a comparison of magnetic form factor plateaus produced by a conventional variational analysis (using an initial basis of n = 8 Structure and transitions of nucleon excitations from lattice QCD 71 operators), with an equivalent extraction via the PEVA technique (with the basis parity-expanded to 2n = 16 operators). We see a significant difference in the plateaus extracted by the two techniques for the singly represented quark sector. If we take the correlated ratio of the extracted values, as shown for a range of kinematics in Fig. 1b, we see a consistent underestimation of the value by the conventional analysis. This shows ~ 20% underestimation of the magnitude of the contributions to the magnetic form factor from the singly represented quark flavour in the conventional analysis. The difference between the two analyses is that the PEVA approach provides additional interpolator degrees of freedom to improve the ground state interpolating field at finite momentum. As such it is clear that the difference between the two extractions is from contaminating states that are present in the conventional analysis but removed by the parity expansion. As such, the PEVA technique is critical for precision measurements of nucleon form factors. — T p* ---p2 ■ p*(1535) • p* (1650) n* n'2 * n*(1535) ▼ n*(1650) _i_i_i_i_ I---- / £ / cS* / / Fig. 2. Comparison between lattice calculations of the magnetic moments of two odd-parity nucleon excitations at mn = 702 MeV and quark model predictions [21-23] for the N*(1535) and N*(1650) resonances. The shaded bands on the left-hand side of the plot indicate the magnetic moments calculated via the PEVA technique in lattice QCD, and symbols denote the quark model predictions. Lattice calculations of the magnetic moments using conventional parity projection are plotted to the right of the vertical dashed line. 3 2 0 2 3 4 Excitations With our local three-quark operators, we observe two low-lying odd-parity eigen-states in the resonance regimes of the N*(1535) and N*(1650). In Ref. [12], we investigate the elastic form factors of these states. There we find that opposite parity contaminations have a large effect on both the electric and magnetic form factors, and the PEVA technique is critical for even a qualitatively correct extraction. 72 Finn M. Stokes, Waseem Kamleh, Derek B. Leinweber 0.0 -0.5 -1.0 < -2.0 -2.5 0.0 0.1 0.2 0.3 0.4 Q2 / GeV2 (a) First odd-parity excitation 0.0 -0.5 -1.0 < -2.0 -2.5 0.0 0.1 0.2 0.3 0.4 Q2 / GeV2 (b) Second odd-parity excitation Fig. 3. Constituent quark model predictions [24] (lines) and PEVA extractions (points) of the ratio of proton to neutron helicity amplitudes at mn = 702 MeV. We focus our investigation at heavier pion masses, where these lattice states lie below the relevant two-particle scattering thresholds on the finite volume. At these masses, we find that these states look remarkably similar to constituent quark model predictions for the N*(1535) and N*(1650). We find the size of these lattice eigenstates to be similar to the ground state nucleons. As shown in Fig. 2, their magnetic moments agree well with constituent quark model predictions for the continuum states. We also present here preliminary results for the transition form factors from the ground state to each of these two lattice eigenstates. These results will be presented in more detail in an upcoming paper. In Fig. 3a we compare the ratio of the transverse helicity amplitudes of the first lattice excitation of the proton and neutron to a constituent quark model prediction for the N*(1535). Taking this ratio allows us to cancel out some of the model dependence of the constituent quark model result. We once again find good agreement between the structure of the lattice eigenstates at the heavier pion masses and the constituent quark '—S—i i I i Structure and transitions of nucleon excitations from lattice QCD 73 model prediction. In Fig. 3b we see a similar result for the second lattice excitation compared to the constituent quark model N* (1650). We see strong agreement between the lattice eigenstates and constituent quark model predictions at these heavier pion masses. This suggests that while the dynamics are much more complicated at the physical point, and the constituent quark model alone does not appear to give a good description of these resonances in nature, as the pion mass increases the constituent quark model describes the excitations rather well. The agreement of the lighter state with the constituent-quark-model N* (1535) is consistent with predictions from Hamiltonian Effective Field Theory (HEFT) [25]. However, the agreement of the heavier state with the constituent-quark-model N* (1650) suggests that future HEFT studies should explore the incorporation of two bare basis states associated with the two different localised states observed herein. In Ref. [12], we also investigate the lowest-lying even-parity excitation of the nucleon observed on the lattice. We find that it has a charge radius approximately 30% larger than the ground state, and a remarkably similar magnetic moment to the ground state. This is consistent with the state being a radial excitation of the ground-state nucleon as seen in Refs. [26,27]. 5 Conclusion The PEVA technique is critical to correctly extracting the form factors of proton and neutron excitations on the lattice. Such extractions give us insight into the structure of the states seen on the lattice. In addition, even for the ground state, we found evidence that the conventional analysis was contaminated by opposite-parity states. For the kinematics considered here, we observe ~ 20% underestimation of the magnitude of the contributions to the magnetic form factor from the singly represented quark flavour at the lighter pion masses. All these results make it clear that the PEVA technique is critical for precision measurements of nucleon form factors and for any study of the structure of nucleon excitations. Acknowledgements This research was undertaken with the assistance of resources from the Phoenix HPC service at the University of Adelaide, the National Computational Infrastructure (NCI), which is supported by the Australian Government, and by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. These resources were provided through the National Computational Merit Allocation Scheme and the University of Adelaide partner share. This research is supported by the Australian Research Council (ARC) through grants no. DP140103067, DP150103164, LE160100051, and DP190102215. References 1. J.-J. Wu, T. S. H. Lee, A. W. Thomas, and R. D. Young, Phys. Rev., vol. C90, no. 5, p. 055206, 2014. 74 Finn M. Stokes, Waseem Kamleh, Derek B. Leinweber 2. Z.-W. Liu, W. Kamleh, D. B. Leinweber, F. M. Stokes, A. W. Thomas, and J.-J. Wu, Phys. Rev., vol. D95, no. 3, p. 034034, 2017. 3. M. Luscher, Nucl. Phys., vol. B354, pp. 531-578,1991. 4. L. Lellouch and M. Luscher, Commun. Math. Phys., vol. 219, pp. 31-44, 2001. 5. B. J. Owen, W. Kamleh, D. B. Leinweber, M. S. Mahbub, and B. J. Menadue, Phys. Rev., vol. D92, no. 3, p. 034513, 2015. 6. R. A. Briceno, J. J. Dudek, R. G. Edwards, C. J. Shultz, C. E. Thomas, and D. J. Wilson, Phys. Rev. Lett., vol. 115, p. 242001, 2015. 7. M. S. Mahbub, W. 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Khemchandani, and H. Dahiya, Eur. Phys. J., vol. A49, p. 11,2013. 24. S. Capstick and B. D. Keister, Phys. Rev., vol. D51, pp. 3598-3612,1995. 25. Z.-W. Liu, W. Kamleh, D. B. Leinweber, F. M. Stokes, A. W. Thomas, and J.-J. Wu, Phys. Rev. Lett., vol. 116, no. 8, p. 082004, 2016. 26. D. S. Roberts, W. Kamleh, and D. B. Leinweber, Phys. Lett., vol. B725, pp. 164-169, 2013. 27. D. S. Roberts, W. Kamleh, and D. B. Leinweber, Phys. Rev., vol. D89, no. 7, p. 074501, 2014. Bled Workshops in Physics Vol. 20, No. 1 p. 75 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 Exotic Baryons in Skyrme Type Models H. Weigel Institute for Theoretical Physics, Physics Department, Stellenbosch University, Matieland 7602, South Africa Abstract. Skyrme type chiral soliton models suggest low-lying exotic baryons with quantum numbers that cannot be represented by three quarks. In these proceedings I discuss properties of their flavor partners in the nucleon channel. 1 Introduction The presentation underlying these proceedings contains three parts discussing exotic baryons in Skyrme type chiral soliton models1. One dealing with light pentaquarks, in particular the extraction of the width from scattering data, the second part discusses the relevance of radial excitations and finally the third part focuses on baryons with a single heavy quark (charm or bottom). The research on the topics covered in parts one and three has distinctively shown that any mean-field treatment is insufficient for a consistent description of exotic baryons. Since 1 have recently summarized this observation in Ref. [2], I will focus on the radial excitations in present proceedings. In chiral soliton models exotic baryon states emerge as elements of higher dimensional SU(3) flavor representations; most prominently the anti-decuplet (10) that, among others, contains the 0+ pentaquark [3]. Yet, these representations also contain baryons with quantum numbers of ordinary three quark states. In particular the mass of the nucleon type element of the 10 is predicted [4] in the regime of the Roper and N(1710) resonances, which in the Skyrme model are understood as radial excitations [5]. Strong mixing effects are therefore expected and the comparison with the established spectrum of excited nucleons will give insight on whether or not 10 baryons are mere artifacts. 2 Collective Flavor and Radial Excitations Skyrme type models are based on effective chiral theories with the basic degree of freedom being the chiral field U G SU(Nf), where Nf is the number of active flavors, here Nf = 3. Baryons are constructed from (static) soliton solutions for the chiral field, U0 = U0 (r). To generate states with baryon quantum numbers from U0, in particular spin and flavor, time dependent collective coordinates, 1 See Ref. [1] for comprehensive review of these models. 76 H. Weigel A(t) € SU(Nf) are introduced via U0(r) —» A(t)U0(r)At(t) and canonically quantized2. To facilitate a study of radial excitations the collective coordinate A(t) for the extension of the soliton is added: Uo(r^ A(t)Uo(A(t)r)At(t). (1) Canonical quantization produces the Hamiltonian 2 1 92 H = Ho - s(A)Ds8(A) with Ho = V (J2,C2; A)- 2^ aX2 ' (2) where the inertial parameter m(A) is computed numerically from U0. The potential V is a sum of terms that are products of coefficients (also computed from U0) and collective coordinate operators like the spin J and the quadratic Casimir operator C2 of SU(3) [6]. Diagonalization of the flavor symmetric component, H0|^,n^} = produces a pertinent basis by finding the radial ex- citations n^ for a given SU(3) representation ^ € {8,10...; 10,27,...}. That is, the basis states factorize: n^} = |^}|n^}. The flavor symmetry breaking part contains an element of the adjoint representation Dab = (1/2)tr [AaAAbA^ with Ai,..., A8 being the Gell-Mann matrices. Computing its matrix elements with respect to the eigenstates of H0 completes the Hamiltonian matrix (M-,nJH|v,nv) = V^n^n - (n^|s(A)|nv)(^|D88(A)|v). (3) Diagonalization yields the baryon states |B,m) = Y.C^m'^,m^} whose eigenvalues are the baryon masses [6]. In figure 1 a typical result for the spectrum relative to the nucleon is compared to models for the excited baryons based on octet-antidecuplet mixing [7,8]. As in Ref. [7] no (new) nucleon type state is seen in the vicinity of 1.6GeV, which is not observed experimentally (so far) but suggested in Ref. [8]. (The models of Refs. [7,8] construct octet and anti-decuplet mixing without specifying the driving dynamics.) However, there are two nearby structures around 1.8GeV. Figure 2 sketches the amplitudes C^^m' in the nucleon channel. Here m = 0 refers to the actual nucleon which is dominated by the octet ground state. The Roper resonance would be identified with m = 1. Surprisingly, the radial ground state from the octet also has the largest amplitude in this channel, though the first radial excitations from the octet, anti-decuplet and 27-plet contribute similarly. The m = 2 state, presumably the N(1710), is mostly composed of the first radial octet and the anti-decuplet ground states. 3 Magnetic Moments It has been shown some time ago that the transition magnetic moment between pure 8 and 10 protons is zero thereby strongly suppressing photo-excitation of the 10 proton [9]. It is therefore important to verify or falsify this observation when 2 Typically U0(r) is of hedgehog structure so that spin is given by flavor generators. Exotic Baryons in Skyrme Type Models 77 E[GeV] 1.8 1.5 this model Ref.[7] |A,2> .......... |Z,2> _ .......... |hs/2,0> |",1> - .......... |N,3> - |N,2> - - |Z,1> _ - |A+1> .......... |0+,O> .......... |N, 1 > Ref.[8] A ","3/2 ........"3/2 Ns - Z2 ........N2 A, Z - Z1 0+ nmm 0+ "3/2 Z2 N 2 Z1 A 0+ N N i Fig. 1. Model prediction for the spectrum of the positive parity spin 1 and | baryons and their radial excitations relative to the nucleon mass. Dashed lines indicate predictions that cannot be (unambiguously) identified with established resonances. 154,1 125,1 81,1 65,1 35,1 27,1 10,1 8,1 m = 0 m = 1 m = 2 Fig. 2. Typical result for the nucleon expansion coefficients | C (N,m)| 1 the important radial admixtures are incorporated. Starting point is the electromagnetic current jke m ) expressed in terms of AUo(Ar)A^ yielding the magnetic moment operator d3jke m ) = a(A) I 033(A) + ^D83(A) +... (4) The (transition) magnetic moments are the matrix elements = (B, m|£t|B', m') = Z CÎBm^CV^mm,)(hID33(A) + D83|v)(m^|a(A)|nv) + ... (5) B Z S 1 N U- 78 H. Weigel In table 1 the resulting data are normalized to the predicted proton magnetic moment in the respective treatments. Here it is = 2.58. There is distinct improvement over the prediction of the rigid rotator approach (RRA), which is a mean-field treatment that does not include radial excitations and has a significantly smaller |p = 2.03 [10] and does not adequately deviate from the U-spin symmetry relations « and |Eo « . The radial part of the wave-function must be sensitive to flavor symmetry breaking to properly reflect the observed deviation. m/Mp bary. rad.ex. expt. RRA n -0.75 -0.68 -0.78 A -0.19 -0.22 -0.35 i+ 0.78 0.86 0.98 i- -0.47 -0.42 -0.39 -0.41 -0.45 -0.76 -0.14 -0.25 -0.32 !0-> A -0.60 -0.58 -0.68 proton neutron m m/Mp M/Mp 1 (Roper?) -0.41 0.40 2 (N1710?) -0.13 -0.08 3 (?) -0.11 -0.09 Table 1. Numerical results for the magnetic moments. Left panel magnetic moments of spin J baryons; right panel transition moments in the nucleon channel. This model result gives good confidence to compute the nucleon channel transition moments. The transition from the first state above the nucleon is of similar magnitude for proton and neutron3. This has to be contrasted to the omission of radial excitations, when the next to leading level in the nucleon channel is a pure anti-decuplet nucleon. In that case the proton transition magnetic moment vanishes [9] while the neutron is of typical size 0.28|p. Indeed some enhancement of the neutron over the proton channel in n-photoproduction has been reported [11], however, most likely this is caused by a negative negative parity structure [12]. The omission of flavor symmetry breaking produces transition moments to the first excitation of — 0.24|, and 0.18|, for the proton and neutron channels. 4 Conclusions In these proceedings I have presented a dynamical mechanism to incorporate radial excitations when describing baryons in Skyrme type models. Only when the mixing of these excitations with members of higher dimensional SU(3) is accounted for, reliable statements on the spectrum of exotic baryons and their flavor 3 The overall signs are subject to the phase conventions on the wave-functions. Exotic Baryons in Skyrme Type Models 79 partners can be made. The present model calculation does not give evidence for an (additional, presumably narrow) nucleon resonance with a mass between 1.6 and 1.7GeV in contrast to the mean-field approach that omits this mixing [13]. Including radial excitations reverses the mean-field results for the nucleon channel transition magnetic moments of Ref. [9]. Acknowledgment The author thanks the organizers for providing this worthwhile workshop and the support to cure his broken arm. This work is supported in part by the National Research Foundation of South Africa (NRF) by grant 109497. References 1. H. Weigel, Lect. Notes Phys. 743 (2008) 1. 2. H. Weigel, Universe 4 (2018) 142. 3. L. C. Biedenharn and Y. Dothan, "Monopolar Harmonics In SU(3)-F As Eigenstates Of The Skyrme-Witten Model For Baryons," Print-84-1039 (DUKE) 4. H. Walliser, Nucl. Phys. A 548 (1992) 649. 5. C. Hajduk and B. Schwesinger, Phys. Lett. 145B (1984) 171. 6. J. Schechter and H. Weigel, Phys. Rev. D 44 (1991) 2916 H. Weigel, Eur. Phys. J. A 21 (2004) 133 7. R. L. Jaffe and F. Wilczek, Phys. Rev. Lett. 91 (2003) 232003. 8. D. Diakonov and V. Petrov, Phys. Rev. D 69 (2004) 094011. 9. M. V. Polyakov and A. Rathke, Eur. Phys. J. A 18 (2003) 691. 10. H. Weigel, Int. J. Mod. Phys. A 11 (1996) 2419. 11. V. Kuznetsov et al., Phys. Lett. B 647 (2007) 23. 12. F. Miyahara et al., Prog. Theor. Phys. Suppl. 168 (2007) 90 I. Jaegle et al., Phys. Rev. Lett. 100 (2008) 252002 13. G. S. Yang and H. C. Kim, Prog. Theor. Phys. 128 (2012) 397 Bled Workshops in Physics Vol. 20, No. 1 p. 80 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 News from Belle on Hadron Spectroscopy M. Bracko University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia and Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia Abstract. In this contribution, recent results on hadron spectroscopy from the Belle experiment are reviewed. All reported results are based on experimental data sample collected by the Belle detector, which was in operation between 1999 and 2010 at the KEKB asymmetric-energy e+ e- collider in the KEK laboratory in Tsukuba, Japan. Even a decade after the end of the experiment, the collected data sample is still used for new measurements. Selection of results from recent Belle publications on hadron spectroscopy is presented in this review, reflecting the scope of the workshop and interest of its participants. 1 Introduction During a decade of succesful operation of both Belle detector[1] and KEKB ac-celerator[2], a large sample of experimental data was collected, corresponding to more than 1 ab-1 of integrated luminosity, with energies around the Y(4S) resonance, but also at other Y resonances, like Y(1S), Y(2S), Y(3S), Y(5S) and Y(6S), as well as in the nearby continuum [3]. The available data has proven to offer excellent opportunities for various measurements, including the ones in hadron spectroscopy, like discoveries of new charmonium(-like) and bottomonium(-like) hadronic states, and studies of their properties. 2 Charmonium and Charmonium-like states The field of charmonium spectroscopy attracted a lot of interest after the discovery of the state X(3872), decaying to J/^n+n-[4], and other so-called "XYZ" states—new charmonium-like states outside of the conventional charmonium picture. Belle continues with studies in this field of research, together with other experiments. Various experimental studies of the X(3872) state determined its JPC = 1++ assignment, and suggested that this state is an admixture of the conventional 23Pi cc state and a loosely bound D°D*° molecular state. If one wants to better understand the structure of X(3872), further studies of production and decay modes for this narrow exotic state are necessary. An example of these experimental efforts is the recent study [5], where Belle performed searches for X(3872) decaying to xc1n°. Simultaneously, a poorly understood state X(3915) was also included in the search. No significant signal was found for any of the News from Belle on Hadron Spectroscopy 81 two states, since only 2.7 ± 5.5 (42 ± 14) events were observed, with a signal significance of 0.3 d (2.3 a-) for the B+ -> X(3872)(-> Xc1n0)K+ (B+ -> X(3915)(-> Xc1n0)K+) decay mode. The upper limits on the product branching fractions B(B+ -> X(3872)K+)xB(X(3872) ^ xc1n0) <8.1x10-6 andB(B+ —> X(3915)K+)x b(x(3915) -> xc1 n0) < 3.8 x 10-5 were determined at 90% confidence level. The null result of the search is compatible with the above mentioned interpretation of the X(3872) state, being the admixture of a conventional charmonium and a DD molecular states. Furthermore, the result for the upper limit of the ratio B(X(3872) -> Xcin0)/B(X(3872) —> J/^n+n-) < 0.97 at 90% confidence level, can be used to constrain the tetraquark/molecular component of the X states. Another analysis, recently performed by Belle on the data sample corresponding to an integrated luminosity of 711 fb-1 and containing 772 x 106BB pairs, focused on a search for the decay B0 —» X(3872)(—» J/^n+n-)y [6]. Rare decays of B mesons are sensitive probes to study possible new physics beyond the Standard Model, which could significantly modify the branching fraction for the B0 —} J/^y decay. Non-charmonium components of the exotic X(3872) would make the B0 —> X(3872)y branching fraction smaller than that of B0 —» J/^y. The performed search resulted in finding no significant signal, so only an upper limit on the product of the branching fractions B(B0 -> X(3872)y) x B(X(3872) -> J/^n+n-) of 5.1 x 10-7 was set at 90% confidence level. The Y(4260) state, also known as ^(4260) [7], is another exotic state, which draws much attention. It was first observed in the initial-state radiation (ISR) process e+e- —» yisrY(4260) by the BABAR collaboration [8], and due to its production in ISR, its quantum numbers are expected to be JPC = 1 . This would make the Y(4260) a natural candidate for a conventional charmonium state with JPC = 1 , but its mass and properties are not consistent with those expected for any of the predicted conventional cc states in this mass region. Instead, the measured properties indicate the exotic nature of the Y(4260) state—it could be an admixture of charmonium and some other structures, like multiquark states or mesonic molecules, it could be a hybrid charmonium, or some other exotic object. In order to understand the structure and properties of the Y(4260) (and some other similar 1 -- states), studies of several decay channels with large data sample are necessary. The most recent example of such a study performed at Belle, is a search for the B -» Y(4260)K, Y(4260) -» J/^n+n- decays using BB pairs collected at the Y(4S) resonance [9]. The observed signal yields for these decays were 179 ± 53+45 events and 39 ± 28+371 events for the charged and neutral B —» Y(4260) K, Y(4260) —> J/^n+n decays, respectively, from fits to the individual decay samples; the first and second uncertainties are statistical and systematic, respectively. The signal significances are obtained to be 2.1a and 0.9a for the charged and neutral decays, respectively, taking into account the systematic uncertainties. The corresponding upper limits on the product of branching fractions, B(B + -> Y(4260)K+) x B(Y(4260) -> J/^n+n-) <1.4 x 10-5 and B(B0 -> Y(4260)K0) x B(Y(4260^ J/^n+n-) <1.7 x 10-5 determined at the 90% confidence level, are the most stringent to date. However, as these results were already based on the complete Belle data sample, more information about 82 M. Bracko the nature of the Y(4260) state can only be obtained by improved measurements with a larger data sample, which will only be available at the Belle II experiment [10]. One of the most recent charmonium-related studies from Belle is a search for the decays B+ -> hcK+ and B0 -> hcK° [11]. The decays B+ -> xc0K+, B+ —> xc2K+ and B+ —> hcK+ are suppressed by factorization. The decays B+ —» XcjK+ have been observed; the current world-average branching fractions are B(B+ -> Xc0K+) = (1.49+0.]5) x 10-4 and B(B+ —> Xc2K+) = (1.1 ±0.4) x 10-5 [7]. While B(B+ —} xc0K+) is smaller than the branching fraction of the factorization-allowed process B(B+ —» xci K+) = (4.84 ± 0.23) x 10-4, it is not strongly suppressed. Under the same assumption, the process B + —» hcK+ was expected to have a similar branching fraction B(B+ —» hcK+) « B(B + —» xc0K+). However, the decays B+ —> hcK+ and B0 —> hcK^ have not been observed before. The reported analysis, which benefits from the large Belle data sample, but also from improved discrimination between background and signal events due to multi-variate analysis, clearly demonstrates the discovery potential at Belle. As a result of this study, evidence for the decay B+ —» hcK+ was found, with a significance of 4.8c, while no evidence was found for B0 —» hcK^. The measured branching fraction for the B+ —» hcK+ decays is (3.7+0^ ± 0.8) x 10-5 while the upper limit for B0 —» hcK^ branching fraction is 1.4 x 10-5 at 90% confidence level. In addition, a study of the ppn+n- invariant mass distribution in the channel B+ —» (p-pn+n-)K+ resulted in the first observation of the decay nc (2S) —} p-pn+n- with more than 12c significance. 3 Results on Charmed Baryons Almost a decade after the end of data taking at Belle, a lot of effort is now invested into studies of charmed baryons. Many results were obtained recently and many analyses are still ongoing. The list of results is quite long and it probably deserves a separate contribution. Here, we will therefore mention just one of the published results [12]—observation of the excited O.- baryon—while other recent publications are only quoted in the reference section ([14],.. .,[25]). In the above mentioned analysis [12], a new hyperon was observed. The observed particle is a candidate for an excited O*- baryon. These baryons comprise three strange quarks, and have zero isospin. This means that O*- —» O-n0 decays are highly suppressed, which restricts possible decays of excited states, so that the largest expected decay modes are EK. This behaviour is analogous to the O0 —» E+K- decays recently discovered by the LHCb Collaboration [13] and confirmed soon after by Belle [16]. The observed new resonance, which is identified as an excited O- baryon, was therefore found in the decay modes O*- —» E0K-and O*- —} E-K°, as expected. The measured mass of the resonance is [2012.4 ± 0.7 (stat) ± 0.6 (syst)] MeV/c2 and its width, r, is [6.4-2.5 (stat) ± 1.6 (syst)] MeV. The mass of the new resonance is 340 MeV/c2 higher than the ground state, which fills the gap in the O- spectrum between the ground state and previously observed excited states. The O*- is seen primarily in the decay of the narrow resonances Y(1S), Y(2S), and Y(3S) (1). The corresponding data samples, collected News from Belle on Hadron Spectroscopy 83 with the accelerator energy tuned for the production of the three mentioned Y resonances, correspond to integrated luminosities of 5.7 fb-1,24.9 fb-1, and 2.9 fb-1, respectively. .Q E o O > (B Lfi OJ c o 03 c E o o 160 140 120 100 80 60 40 20 350 300 250 200 150 100 50 2 2.05 2.1 M(S K) GeV/c2 Fig. 1. The (a) S0K- and (b) invariant mass distributions in data taken at the energies of Y(1S), Y(2S), and Y(3S) resonances. The curves show the result of a simultaneous fit to the two distributions with a common mass and width. 4 Summary and Conclusions Many new particles have already been discovered during the operation of the Belle experiment at the KEKB collider, and some of them are mentioned in this report. Although the operation of the experiment finished almost a decade ago, data analyses are still ongoing and consequently more interesting results on char-monium(-like), bottomonium(-like) and baryon spectroscopy can still be expected from Belle in the near future. The results are eagerly awaited by the community and will be widely discussed at various occasions, in particular at workshops and conferences. Still, the era of the Belle experiment is slowly coming to an end. Further progress towards high-precision measurements—with possible experimental 84 M. Bracko surprises—in the field of hadron spectroscopy are expected from the huge experimental data sample, which will be collected in the future by the Belle II experiment [10]. Actually, this future has already started, since the completed Belle II detector began its operation at the SuperKEKB collider in March 2019. References 1. Belle Collaboration, Nucl. Instrum. Methods A 479,117 (2002). 2. S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods A 499,1 (2003), and other papers included in this Volume. 3. J. Brodzicka et al., Prog. Theor. Exp. Phys., 04D001 (2012). 4. Belle Collaboration, Phys. Rev. Lett. 91, 262001 (2003). 5. Belle Collaboration, Phys. Rev. D 99,111101(R) (2019). 6. Belle Collaboration, Phys. Rev. D 100, 012002 (2019). 7. M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018). 8. BABAR Collaboration, Phys. Rev. Lett. 95,142001 (2005); Phys. Rev. D 86, 051102 (2012). 9. Belle Collaboration, Phys. Rev. D 99, 071102(R) (2019). 10. Belle II Collaboration, Belle II Technical design report, [arXiv:1011.0352 [physics.ins-det]]. 11. Belle Collaboration, Phys. Rev. D 100, 012001 (2019). 12. Belle Collaboration, Phys. Rev. Lett. 121, 052003 (2018). 13. LHCb Collaboration, Phys. Rev. Lett. 118,182001 (2018). 14. Belle Collaboration, Phys. Rev. D 97, 012005 (2018). 15. Belle Collaboration, Phys. Rev. D 97, 032001 (2018). 16. Belle Collaboration, Phys. Rev. D 97, 051102 (2018). 17. Belle Collaboration, Phys. Rev. D 97, 072005 (2018). 18. Belle Collaboration, Phys. Rev. D 97,112004 (2018). 19. Belle Collaboration, Phys. Rev. D 98,112006 (2018). 20. Belle Collaboration, Eur. Phys. J. C 78, 252 (2018). 21. Belle Collaboration, Eur. Phys. J. C 78, 928 (2018). 22. Belle Collaboration, Phys. Rev. D 100, 032006 (2019). 23. Belle Collaboration, Phys. Rev. D 100, 031101 (2019). 24. Belle Collaboration, Phys. Rev. Lett. 122, 072501 (2019). 25. Belle Collaboration, Phys. Rev. Lett. 122, 082001 (2018). Bled Workshops in Physics Vol. 20, No. 1 p. 85 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 The enigmatic A(1600) resonance B. Golli Faculty of Education, University of Ljubljana and Jozef Stefan Institute, 1000 Ljubljana, Slovenia Abstract. Our recently proposed model of the A(1600) resonance, in which the dominant component is a quasi-bound state of the A(1232) and the pion, is confronted with a similar model of the N*(1440) resonance as its counterpart in the P11 partial wave. We stress an essentially different mechanism responsible for generating the two resonances. The two low-lying resonances in the P11 and P33 partial waves, the Roper resonance (N*(1440)) and the A(1600) resonance, have been attracting special attention due to their relatively low masses compared to the prediction of the quark model in which they figure as the first radial excitations in the respective channel, and have been considered as candidates for dynamically generated resonances. In order to understand the mechanism of their formation we study these two resonances in a chiral quark model, which may produce either a genuine resonance by exciting the quark core, or a dynamically generated resonance involving a baryon-meson quasi-bound state. We use a coupled channel approach involving the nN, nA, and ctN channels which — based on our previous experience — dominate the intermediate energy regime in the P11 and P33 partial waves. The Cloudy Bag Model (CBM) is used to fix the quark-pion vertices while the s-wave CT-baryon vertex is introduced phenomenologically with the coupling constant gCT as a free parameter. Labeling the channels by a, |3,y, the Lippmann-Schwinger equation for the meson amplitude x«y for the process y —» a can be cast in the form Xay(k iX) ky) = K ay( P ' The half-on-shell pion amplitude consists of the resonant and non-resonant part, Kaß(ka,k)xßT(k,kT) w(k)+ Eß(k) — W • Xay(k,kT) = cyRVaR(k)+ Day(k,ky), (2) with the non-resonant part Day(k, ky) satisfying the same Lippmann-Schwinger equation, while the dressed vertex VaR (k) satisties the Lippmann-Schwinger equation with the same kernel and the bare vertex for the non-homogeneous part. Approximating the kernel K by a separable form, the integral equations reduce to a system of linear equations which can be solved exactly. The resulting amplitude is proportional to the K matrix which, in turn, determines the scattering T matrix. The Laurent-Pietarinen expansion is finally used to extract the information about the S-matrix poles in the complex energy plane. 86 B. Golli The formation of the Roper resonance (N*(1440)) is studied in Ref. [1], confronting two mechanisms for resonance formation: the explicit inclusion of a resonant three-quark state in which one quark is promoted to the 2s state, and the dynamical generation in the absence of the resonant state. In both cases the nucleon pole is explicitly included. While the p-wave nN interaction is repulsive in the P11 channel, the s-wave oN interaction is attractive, and is able to support a (quasi) bound state for sufficiently strong gCT. The resulting mass of the resonance is close to the PDG value in a relatively wide interval of gCT, while its width is smaller than the PDG value and drops with increasing gCT. Including a three-quark resonant state, the mass of the resonance remains almost the same, while its width increases and comes very close to its PDG value (see Table III in [1]). The result is rather insensitive to the mass of the three-quark resonant state, which allows us to use a value around 2 GeV, in agreement with the quark-model ordering of the 2s and 1p states, as well as with the recent results of the lattice calculations [2,3] which have not found a sizable three-quark component below ~ 1.7 GeV. We conclude that while the mass of the S-matrix pole is determined by the dynamically generated state, its width and modulus are strongly influenced by the three-quark resonant state. This conclusion is further supported by a smooth evolution of the S-matrix pole in the complex energy plane as the coupling of the o as well as of the pion to the quark core is gradually increased on (see Fig. 1). Starting with two bare masses of 1750 MeV and 2000 MeV, both curves end up almost at the same point with the mass and width consistent with the PDG values. Fig. 1. Evolution of the N * ( 1440) mass (Re W) and the width (proportional to the radius of the circle) as a function of the interaction strength for two bare masses of the three-quark configuration, 1750 MeV and 2000 MeV; g/g0 denotes the reduction factor, equal for each coupling constant. The radius at g/g0 = 1 corresponds to Im W = 180 MeV. ci 2000 1900 1800 1700 1600 1500 1400 1300 N*(2.0 GeV) N*(1.75 GeV) 0.2 0.4 0.6 g/go 0.8 0 1 Though we might expect that, because of apparently the same three-quark configuration, the situation with the A(1600) is similar to that with the N*(1440) resonance, this is not the case. One important difference is the nature of the p-wave nN interaction which is attractive in the P33 partial wave, in contrast to its repulsive character in the P11, P13, and P31 waves. Furthermore, the analog of the oN system, the oA(1232) system, turns out to make a sizable contribution to the scattering amplitude only above 1700 MeV, and hence the o plays a minor role in the formation of the A(1600) resonance. In [5] we therefore consider only the The enigmatic A(1600) resonance 87 nN and the nA channels. Since the nN coupling constant is fixed by the behavior of the scattering amplitudes near the threshold, the only free parameter in the underlying model (CBM) is the bag radius R which is inversely proportional to the cutoff energy; for the value of R = 0.8 fm, leading to the most consistent results for the nucleon as well as for the low lying resonances, it corresponds to « 550 MeV. Fig. 2. Evolution of the poles as a function of the bag ra- Already a few years after the discovery of the A(1232) resonance, it was conjectured that this resonance arises as a consequence of the attraction in the nN system at sufficiently strong cutoff [6]. In our model we do observe a resonance in the nN system manifesting itself as a pole in the complex energy plane at a mass around 1200 MeV, with a width that decreases with increasing interaction strength (decreasing R) (orange curve in Fig. 2). For R = 0.123 fm the mass and the width reach the values which agree well with the PDG values, and for R = 0.050 fm the system becomes bound. We next include the A (in addition to the nucleon) as the u-channel exchange particle in the kernel, and solve (1) for the nonresonant amplitude D. Besides the pole at around 1200 MeV another pole slightly below 1400 MeV emerges (green curves in Fig. 2). The second pole is dominated by the nA configuration and can be interpreted as a progenitor of the A(1600) resonance. We next include a three-quark state corresponding to the A(1232) in the s-channel and fix its bare mass such that the resulting Breit-Wigner mass (i.e., the zero of Re T) appears at 1232 MeV. With decreasing R the resonant state mixes more and more strongly with the lower dynamically generated state, forming the physical A(1232). The latter component dominates below R = 0.2 fm, nonetheless, the mass and the width of the resonance pole remain constant (red curves in Fig. 2) and stay close to the PDG value. The upper dynamically generated resonance is pushed toward a slightly higher mass and acquires a larger width. In the physically sensible region around R « 0.8 fm, the mass and the width come close to the PDG values for the A(1600) resonance. The attribution of this pole to the dius in the P33 partial wave in three different approximations: (i) including only the nucleon and the pion (orange curve and circles), (ii) including the nucleon and the A but without a resonant state (green), (iii) with the A resonant states (red). The width of the resonance —2Im W is proportional to the radius of the circle. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 R [fm] 88 B. Golli A(1600) resonance is, however, not justified for smaller R, where its mass keeps increasing, and, in addition, another branch emerges, approaching the upper dynamically generated resonance. We finally add a bare (1s)2(2s) configuration representing the first radial excitation of the A(1232). In the harmonic oscillator model, its mass is expected to lie ~ 1 GeV above the (1s)3 configuration, so we fix its (bare) mass at 2.2 GeV, while its coupling is taken from the CBM. Apart from the two resonances discussed above, the third resonance emerges with a mass (Re W) close to the bare value. Increasing the strength of the interaction (decreasing R) we notice that it stays almost constant and — at least in the physically relevant regime of R's — well separated from the other two resonances. Fig. 3. Evolution of the poles in the model including two resonant states with the second state at the bare mass of 2.2 GeV (blue curves) and at 2.0 GeV (violet), respectively, compared with the model involving A alone (red, the same curve as in Fig. 2). 0.9 0.8 0.7 R [fm] 0.6 0.5 1 We can therefore conclude that the radially excited quark state plays a very minor role in the formation of the A(1600) resonance, which in our model turns out to be primarily a quasi-bound state of A(1232) and the pion. This mechanism is therefore fundamentally different from that responsible for the formation of the N* (1440) resonance, discussed above, and originates in the different nature of the pion interaction in the two partial waves. This work has been done in collaboration with H. Osmanovic (Tuzla) and S. Sirca (Ljubljana). References 1. B. Golli, H. Osmanovic, S. Sirca, and A. Svarc, Phys. Rev. C 97, 035204 (2018). 2. C. B. Lang, L. Leskovec, M. Padmanath, S. Prelovsek, Phys. Rev. D 95, 014510 (2017). 3. A. L. Kiratidis et al., Phys. Rev. D 95, 074507 (2017). 4. M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98 , 030001 (2018). 5. B. Golli, H. Osmanovic, S. Sirca, Phys. Rev. C 100, 035204 (2019). 6. G. F. Chew and F. E. Low, Phys. Rev. 101,1570 (1956). Bled Workshops in Physics Vol. 20, No. 1 p. 89 A Proceedings of the Mini-Workshop Electroweak Processes of Hadrons Bled, Slovenia, July 15-19, 2019 A phenomenological lower bound for the E+c+ mass Mitja Rosina Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, P.O. Box 2964, 1001 Ljubljana, Slovenia and J. Stefan Institute, 1000 Ljubljana, Slovenia Abstract. We show that a simple interpolation between mesonic binding energies can give a good semiquantitative binding energy of the cc diquark and the baryon. The mass of the baryon is almost insensitive to widely different choices of the constituent quark masses. 1 Introduction After the discovery of the E++ baryon at LHCb, there is a strong interest to verify whether the quark models which have been successful for light and single-heavy hadrons apply also to double-heavy hadrons; in particular, how rich spectrum we can expect. It is important to check whether we may use the same effective quark-quark interaction (apart from the colour factor and the mass-dependent spin-spin term): Vuu = Vcu = Vcc = Vce = Vbu = Vbb = Vbb. For this purpose it is instructive to study some phenomenological models even if the results are only semiquantitative. The present study is based on two assumptions: (1) The quark-quark interaction in colour-triplet state is half the quark-antiquark interaction in colour-singlet state. (2) The ccu baryon can be treated as a two-body system, the cc diquark plus the u quark, similar to the cu or bu meson. These assumptions have been made already by several authors, for example [1,2]. The purpose of this presentation is to show a nice trick how to obtain easily the binding energies of meson-like systems by a simple interpolation between mesonic data [3]. 2 The cc diquark interpolated between mesons We compare the nonrelativistic Schrodinger equations for an (alb) meson in the colour singlet state and for an (ab) diquark in a colour antitriplet state (with twice weaker interaction): 2m, + V alb alb ^ = Eab ^ = F(mab 2 P 90 Mitja Rosina 2m; + Vab ab 2m ab + 2 Vab P2 2(mab/2) + V alb = Eab ^ = 1 F(1 mabH- Here the reduced masses are mab = ma mb/ (ma + mb) and mab = ma mb/(ma + mb), respectively. The binding energy F(m) is a smooth function of m as illustrated in Fig. 1. Phenomenological binding energies of mesons are obtained from experimental meson masses M and model vales of constituent quark masses: Eab = Mab — ma — mi. The diquark masses are then predicted (Table 1). The trick is to take for the diquark binding energy 2F( 1 mab), according to the above Schrodinger equation. The constituent quark masses in Fig. 1 and Table 1 are taken from Bhaduri [4]: mu,d,s,c,b = 337, 337, 600, 1870, 5259 MeV, and in Table 1 also from Karliner and Rosner [1]: mu,d,s,c,b = 310, 310, 483,1663, 5004 MeV. 2 2 P P \F{m) 0.0 [GeV] -0.1 -0.2 -0.3 -0.4 -0.5 0.5 1.0 1.5 2.0 2.5 rri [GeV] Fig. 1. The meson binding energy F(m), multiplied by 1, as a function of the reduced mass m = mab. The diquark binding; energies lF(lmab) are then predicted by interpolation. (From [3]). 3 The binding of tine E++ baryon The (cc)u baryon is treated as a two-body system. The reduced mass is m = mu Mcc/(mu + Mcc), where Mcc = 2mc + 2F(2mcc) and the binding energy between the u quark and the (cc) diquark E(cc)u = F(m) is obtained by interpolation in Fig. 1 or Table 1. The mass of the E+++ baryon is then M(ic)u = Mcc+mu + E(cc)u =3605 (3596) MeV for the choice of constituent masses of Badhuri (or Karliner-Rosner). A phenomenological lower bound for the mass 91 Table 1. The interpolation between mesons. The tilde means spin average, A is the difference between the vector and scalar mesons, m is the reduced mass for mesons and half the reduced mass for diquarks; F is the meson or baryon binding energy and twice the diquark binding energy. Reduced masses refer to the constituent quark masses of Bhaduri [4] or Karliner-Rosner [1], respectively. Energies and masses are in MeV. In the 6th and 9th column are predictions for the diquark and double heavy baryons. Meson mass A m Bha F mass predict m Kar-Ros F mass predict D 1973 141 286 -234 261 0 B 5314 46 317 -282 292 0 Ds 2076 144 454 -394 374 -70 BS 5403 48 539 -456 440 -84 i 3069 113 935 -671 832 -257 Y 9445 61 2630 -1073 2502 -563 cc 467 -405 3538 416 -80 3286 bb 1315 -819 10108 1251 -383 9817 (cc)u 308 -268 3605 283 0 3596 (bb)u 317 -282 10163 301 -4 10123 4 The hyperfine correction So far, spin averages were taken for the diquark and baryon binding energies. The hyperfine splitting is obtained from the experimental differences between vector and scalar mesons. The cc diquark (S = 1) is therefore heavier by (1/4)A(^)/2 = 113 MeV/8 = 14 MeV. (The extra (1/2) comes from the fact, that the potential in cc colour triplet state is twice weaker than in mesons.) On the other hand, the (cc)u (S = 2) baryon is lighter by « A(D) (1870/3552) = -74 MeV. (The latter factor takes into account that the spin-spin interaction is inversely proportional to both masses, so instead of the u quark mass in the D meson one takes the (cc) mass. Also, it is convenient that the reduced mass of (cc)u is close to that of D and Ds mesons, so the interpolation is trivial.) The result for the E++ mass is then 3545 MeV (Badhuri quark masses) or 3539 MeV (Karliner-Rosner quark masses). 5 A note on the binding energy of the DD* dimeson We cannot estimate the binding energy of the DD* dimeson in the same way since the (cc)ub ("tetraquark" or "atomic" or " He-like") configuration is about 100 MeV above the D+D* threshold [3]. This is then only a minor configuration, the main configuration is a DD* "molecule", with a covalent bond like the H2 92 Mitja Rosina molecule. In the restricted 4-body space with the two c quarks far apart and a general wavefunction of u and d the energy is also above the D+D* threshold, as presented by several authors. Only combining both types of configurations brings the energy below the threshold, as shown by Janc and Rosina [5-7]. In the nonrelativistic calculation with the one-gluon exchange potential (including the chromomagnetic term) plus the linear confining potential they obtain the binding energy (DD*) - (D + D*) = - 2.7 MeV . The model parameters (Grenoble AL1) [8] fitted all relevant mesons and baryons and a rich 4-body space was used (Gaussian expansion at optimized distances, with 3 types of Jacobi coordinates). We pose an important question ("to be discussed at the next Bled Workshop") whether the pion and sigma clouds between the u and d antiquarks can increase binding, in analogy with the deuteron. Is there a double counting? Would it be necessary to refit the model parameter so much that this extra binding would be compensated? If, however, the binding really becomes much stronger, at least below -6 MeV, the DDn decay channel would be closed, the DD*system would live longer and would be easier to be recognized in experiment. 6 Conclusion The phenomenological binding energies of the cc diquark and the E++ baryon can be obtained by interpolation between the mesonic data. The mass of the E++ baryon is a lower bound, further corrections (eg. the Coulomb energy and the finite size of the cc diquark) would raise it, possibly close to the experimental value. It is instructive to see that the final result depends only very weakly on the choice of quark constituent masses. In the binding energy, larger constituent masses (larger by as much as 200 MeV) are compensated by a stronger attractive potential. References 1. M. Karliner and J. L. Rosner, Phys. Rev. D 90 (2014) 094007. 2. M. Karliner and J. L. Rosner, Bled Workshops in Physics 20, No. 1 (2019) , these Proceedings; also available at http://www-f1.ijs.si/BledPub. 3. D. Janc and M. Rosina, Few-Body Systems 31 (2001) 1-11; also available at arXiv:hep-ph/0007024v3. 4. R. K. Bhaduri L. E. Cohler, Y. Nogami, Nuovo Cim. A65 (1981) 376. 5. D. Janc and M. Rosina, Few-Body Systems 35 (2004) 175-196; also available at arXiv:hep-ph/0405208v2. 6. M. Rosina and D. Janc, Bled Workshops in Physics 5, No. 1 (2004) 74; also available at http://www-f1.ijs.si/BledPub. 7. M. Rosina, Bled Workshops in Physics 18, No. 1 (2017) 82; also available at http://www-f1.ijs.si/BledPub. 8. B. Silvestre-Brac, Few-Body Systems 20 (1996) 11. Bled Workshops in Physics Vol. 20, No. 1 p. 93 A Proceedings of the Mini-Workshop Electroweak Processes ofHadrons Bled, Slovenia, July 15-19, 2019 Measurement of GA and the GDH sum rule at high energies at Jefferson Lab: two proposals S. Šircaa'b a Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia b Jožef Stefan Institute, Jamova 39,1000 Ljubljana, Slovenia Abstract. We present two developing experimental proposals for measurements to be performed by using electron scattering, with TJNAF (Jefferson Lab) as the most likely facility: a clean measurement of the nucleon axial form-factor, G A, and a measurement of the high-energy contribution to the Gerasimov-Drell-Hearn (GDH) sum rule. The work on GA is done in collaboration with A. Deur (Jefferson Lab) and C. M. Camacho (IPN-Orsay), and the GDH effort is pursued in collaboration with A. Deur, M. Dalton (Jefferson Lab) and J. Stevens (College of William & Mary). 1 Clean measurement of GA The nucleon electro-magnetic form-factors, GE(Q2) and GM(Q2), parameterize the (nucleon) electro-magnetic current operator, and they are well known over a range of Q2 from e-p and e-"n" scattering. With certain approximations, they can be considered as Fourier transforms of spatial distributions of nucleon charge and magnetization. On the other hand, the axial and pseudoscalar form-factors, Ga(Q2) and GP(Q2), entering the axial current, N(p ') qY|Y5y q N(p))= U(p ') Y|Ga(Q2) + 2, , (p!-pv Gp (q2 ) 2M p(Q ' are less well known. The axial form-factor, in particular, can be thought to probe the spatial distribution of the nucleon spin, as can be seen from the terms containing a appearing upon a non-relativistic reduction of the axial current: CT CT • p CT • p ' CT • p CT • p ' CT E + M' E' + M' E + M E' + M The axial form-factor is conventionally parameterized in the so-called "dipole" form, i. e. by using the same traditional functional form as used in the electromagnetic form-factors: Ga(Q2) = Ga(0) 1 + 01 Ma2 Ga(0) = gA « 1-27, (1) OC 2 94 S. Sirca where gA is the axial coupling constant and MA ~ 1 GeV is an adjustable "axial mass" (cut-off parameter). Different (and better justified) parameterizations exist, e. g. based on axial-vector dominance, large Nc and high-energy-QCD constraints: 2 1 Ga(Q ) = ^ cn 1 + Q2/m2 . Such a representation uses a sum of "monopole" forms, with the index n running over isovector/axial-vector mesons (a1, a',...), and cn = fn gnNN/gA, where fn is the vacuum amplitude of meson n and gnNN its coupling to the nucleon [1]. 1.1 Existing determinations of GA Thus far GA(Q2) has been extracted by using two methods: elastic or quasi-elastic neutrino scattering, and electron scattering. In the first case one measures the cross-sections for the processes vn —> l-p and Vp —> l+n (in nuclei), da G2 M2 cos2 9c dQ2 8n E2 A(Q2) t B(Q2) M2 M2 + C(Q2) (s - M2)2 M4 where A(Q2), B(Q2) and C(Q2) are known functions of Ge(Q2), Gm(Q2) and Ga(Q2). The axial form-factor is then determined by fitting the Q2-dependence of the cross-section; the cut-off parameter MA is then typically extracted by assuming the dipole form of GA(Q2) (see [2] and references therein). In the second case, one exploits the p(e, e'n+)n process near threshold [3], for which the cross-section can be written as da _ r day _ „ dEe dne dan _ v dan ' _ v daT + y daL dan + £l dn^j where rv is the virtual photon flux. The longitudinal part of the cross-section probes Fn(Q2), while its transverse part is sensitive to GA(Q2) and, in turn, to the axial RMS radius, (rA2) _- 6 dGA(Q2) Ga (0) dQ2 Q2 = 0 12 MA2 It is well known from xPT [4] that the axial radius picks up a correction due to pion loops, such that the "true" axial radius (measured in neutrino scattering) becomes modified in electro-production experiments: (rA2^ (rA2) + 3 64f2 1 - 12 ' n2 (2) As suggested by the extractions shown in Fig. 1, this indeed seems to be the case: the neutrino experiments yield a world average of (MA) = (1.026 ± 0.009) GeV, while the pion electro-production experiments give (MA) = (1.062 ± 0.015) GeV. There is an « 2.5 ct difference in (MA) between the two extraction methods, but one should not overlook the large statistical and systematic uncertainties and possible data inconsistencies. In particular, the MiniBooNE collaboration, performing a state-of-the-art neutrino scattering experiment, has reported values as high as MA « 1.35 GeV! s Measurement of GA and the GDH sum rule 95 CERN HLBC 64 CERN HLBC 67 CERN SC 68 CERN HLBC 69 ANL 69 ANL 73 ANL 77 CERN GGM 77 CERN GGM 79 BNL 80 BNL 81 ANL 82 IHEP 82 Fermilab 83 Fermilab 84 IHEP 85 BNL 88 IHEP SKAT 88 CERN BEBC 90 BNL 90 IHEP SKAT 90 NuTeV 04 K2K SciFi 06 MiniBoone 07 K2K SciBar 08 NOMAD 08/09 MiniBoone 10 MINERvA 13 AVERAGE 0.4 0.6 0.8 1 1.2 1.4 1.6 Ma [GeV] Frascati 70 Frascati 72 DESY 73 Daresbury 75 Daresbury 76 DESY 76 Kharkov 78 Olsson 78 Saclay 93 Mainz 99 AVERAGE 0.6 0.8 1 1.2 1.4 1.6 Ma [GeV] Fig. 1. Extractions of the axial mass parameter from neutrino experiments (top panel) and electron scattering experiments (bottom panel). The difference in their averages, (MA) = (1.026± 0.009) GeV and (Ma) = (1.062± 0.015) GeV, respectively, may have their origin in the chiral correction (2) — but may also hint at a limitation of the dipole parameterization. 96 S. Sirca 1.2 Proposed measurement of GA by using inverse (3 decay Clearly our knowledge of the axial form-factor would benefit from a third, independent and ideally cleaner, way to access GA. The theoretically cleanest way to access GA (but, as it turns out, experimentally very challenging) is through the weak interaction, as in neutrino experiments — but it can also be probed in weak electron scattering, i. e. in inverse |3 decay shown in Fig. 2: V(G)",p") ♦ W n(e',pn) Fig. 2. Kinematics of inverse (3 decay used to access G a in an electron scattering experiment, with detection of neutrons the final state. The weak charged-current cross-section is given by do- „, Gl COS2 0c O>' = M- F da)' 7T CD cos {- f2 + 2fl+n^f3 J sin y where the structure functions fi, f2 and f3 are known functions of the electromagnetic form-factors and Ga - In contrast to pion electro-production experiments, the extraction of Ga from this purely weak process is model-independent, and with recent advances in polarized beams high precision is possible. The main experimental challenges are: tiny cross sections (on the order of « 10~40 cm2/sr), neutron detection with accurate kinematics; and (very) large electro-magnetic backgrounds. The strategies to deal with these challenges are presently being developed, but we will certainly wish to exploit the available high-intensity polarized electron beams at either JLab or MAMI, in conjunction with a long LH2 target; we would wish to remain at low beam energy (less than « 120 MeV) in order to stay below the pion production threshold; and design a suitable backward kinematics to enhance the weak cross-section (forward neutrons). The beam must be polarized and pulsed so that the electro-magnetic background can be cleanly removed: the weak process has a 100 % asymmetry while the electro-magnetic process has a vanishing asymmetry, and they can be separated on a pulse-by-pulse basis. So far several facilities have been considered where this experiment could take place: MESA at Mainz, FEL at JLab, Hall D tagger at JLab, at the JLab injector, or at Cornell. Each has its particular instrumental constraints, its own pros and cons regarding beam conditions and available infrastructure. Regardless of Measurement of GA and the GDH sum rule 97 the peculiarities of the setup, we will need to remove the scattered electrons (Moller, nuclear scattering) by means of a sweeper magnet; reduce the prompt electro-magnetic radiation (y-flash, electrons) by timing cuts; reduce the background from the target cell window by minimizing window thickness and using a backwards veto detector. We do possess preliminary background estimates, and a detailed Monte Carlo simulation is underway. Assuming 100 % efficiency and no further backgrounds, the precision of the extracted GA that we could achieve in about 2 months of running (order of magnitude estimate) is indicated in Fig. 3. Q2 [GeV2] Fig. 3. The expected precision of the extracted GA with ~ 2 months runtime at a typical high-luminosity facility. The MA = 0.84 GeV and MA = 1.35 GeV curves correspond to the dipole parameterization (1) with the two rather extreme axial masses (one far below and one far above the world average). If nothing else, with the shown precision we should be able to reject or confirm the dipole form itself. 2 Ascertaining the high-energy behavior of the GDH integrand The Gerasimov-Drell-Hearn (GDH) sum rule is a sum rule that relates the energy-weighted difference of the spin-dependent cross-section for photo-production off a given target to the spin (S) and anomalous magnetic moment (k) of that target: dv 4aSn2 k2 Vthr (aV2 - ai/2) V = M2 where a is the fine-structure constant. This is a generic QFT prediction valid for any type of target. In its derivation, one relies on causality, unitarity, Lorentz and gauge invariances. In addition, one assumes that in the forward Compton scattering amplitude, g^M1 (v,0 = 0) = f(v)e'* • e + i g(v)ff • (e" x e) , the spin-dependent amplitude g(v) vanishes at large v to derive the dispersion relation, and that Im g(v) decreases fast enough with v (faster than ~ 1/ log v) for 98 S. Sirca the integral to converge. Note that the integral of the unpolarized cross-section, J(°3/2+°"i/2) dv, without the 1/v weight, does not converge. Looking at Fig. 4 which shows a prediction of the running GDH integral to very high energies one could claim that the sum rule is saturated already at v « 3 GeV but in fact no measurements exist above that energy: all existing experiments (at LEGS, MAMI and ELSA) were performed below it. The polarized cross-section at large v is unknown, yet it is usually expected to be described by Regge theory: it considers isoscalar (p + n) and isovector (p — n) contributions to o3/2 — fi/2 as coming from different meson families: f1 (1285) and a1 (1260), respectively, resulting in the parameterization Ao(p±n) = o3/2 — o1/2 = c2 safi-1 ± c1saa1 -1 , where s = 2Mv + M2, afl and aQl are the Regge intercepts of f1 (1285) and a1 (1260) trajectories, respectively, and c1 and c2 are parameters. cut-off [GeV] Fig. 4. The value of the GDH integral on the proton as a function of the upper integration bound. (Figure taken from [5].) If the sum rule fails, its derivation implies that this would occur at high energies, and there are several conceivable violation mechanisms [6]. For instance, the appearance of a fixed J = 1 pole of the Compton amplitude in the complex angular-momentum plane or the existence of an anomalous charge-density commutator, i. e. [J0(x), J(y)]e.t. = 0 would both cause the sum rule to fail; other, more exotic possibilities have been proposed. Measurement of GA and the GDH sum rule 99 2.1 Experimental strategy The main task of the experiment currently being devised is to measure the energy dependence of the GDH integrand at high energies for both proton and neutron (deuteron) to allow for isospin separation. Assuming °3/2 - = avb (for a given target), the primary goal is to get b, without a need to extract an accurate a. Initially, we would measure only the yield difference, N3/2 — Ni/2, and consider proper normalization (absolute cross-sections) later on. The ideal facility to run the proposed experiment would be Hall D at JLab with a circularly polarized tagged photon beam, longitudinally polarized target and large solidangle (« 4n) detector: this setup would allow us to measure Act(v) at high v where no data exist, and to cover four times the existing v range (3 GeV —» 12 GeV). 2.2 Impact of the proposed experiment Intercept of the ai Regge trajectory The high-energy behaviors of the isovector (non-singlet) and isoscalar (singlet) cross-section differences are driven by the ai (1260) and f1 (1285) Regge trajectories, From DIS data one typically extracts aai « 0.4, af, « —0.5, while a recent fit [7] yields aai « 0.45, afl « —0.36. A naive Regge expectation gives aai « —0.27, afl « —0.32, so there appears to be a discrepancy in the a1 intercept between the two extractions. Measuring Act at high v for both proton and neutron targets would help to remove this uncertainty. Spin-dependent Compton amplitude Figure 5 shows the real and imaginary parts of the spin-dependent Compton amplitude g. The imaginary part is measured directly in a GDH experiment as v Im g(v) = - — Act(v) . The real part, however, is given by a dispersion relation, v 'Act(v ') Re g(v) = - ^P „/2 dv ' and is therefore very sensitive to the quality of the integrand. If both Re g(v) and Im g(v) were known precisely enough (and given f(v) which is well measured), the two complex amplitudes could be used to determine the forward-scattering (9 = 0) quantities _dCT dn U|2 , I 12 =|f| + |g| ^2z|e=o — e=o fg* - f*g |f|2 + Igl2 2 v 100 S. Sirca > 2 GeV, hence a precise measurement of Ao(v) in the v range up to about 10 or 12 GeV could significantly reduce the uncertainty on I2z. Polarizability correction to hyperfine splitting in muonic hydrogen The third impact of the proposed measurement is related to the "proton radius puzzle", specifically to the effect of proton structure on the hyperfine splitting of the nS levels in muonic hydrogen, EHFs(nS) = [1 + Aqed + AWeak + Astructurel EFermi(nS) . The proton-structure correction can be split into three terms: the Zemach radius, the recoil contribution, and the polarizability contribution, Astructure = AZ + Arecoil + Apol • Measurement of GA and the GDH sum rule 101 At present, the relative uncertainties of the three terms are 140 ppm, 0.8 ppm and 86 ppm, respectively, which need to be put into the perspective of the forthcoming PSI measurement of the hyperfine splitting whose precision is expected to be as low as 1 ppm. Our proposed measurement can contribute to the uncertainty reduction in the third correction term. It can be written as Zam Apol = -[Si + §2] , 2n(1 + k)m where m is the electron mass. Here S1 involves an integral of the polarized distribution function g1 (x, Q2) over both x and Q, while S2 involves a similar integration of g2(x, Q2): see [8] for explicit formulas. Since g1 at low Q is essentially the GDH integrand, 4na2 ( Q2 V2 g2 ct1/2 — ct3/2 = m g1 a precise measurement of Act would constrain S1. To calculate S1, one indeed needs the Q2 dependence of g1, but the integrand is weighted by 1/Q3, thus knowing the value at Q2 = 0 would stabilize the integration. This is badly needed, as the above mentioned 86 ppm uncertainty needs to be brought down to the 1 ppm level, and this implies that our knowledge of g 1 needs to be improved by two orders of magnitude! Transition from polarized DIS to diffractive regime The proposed experiment would also have the capability to explore the transition between DIS and low-x regime of diffractive scattering. This regime has been investigated e. g. at HERA, but only in the unpolarized case. Such processes are traditionally described in terms of a diquark picture: a hard y* hadronizes into a qq pair of coherence length 1/(xM), with high Q2 dominated by gluon exchange and low Q2 dominated by Pomeron/Reggeon exchange as shown in the Figure: The spin-0 Pomeron couples to the proton components irrespectively of their helicity, i. e. controls unpolarized diffractive scattering, while double-polarized ep scattering filters out Pomeron exchange to reveal the non-singlet Reggeon exchange. This is relevant for the physics of the envisioned Electron-Ion-Collider (EIC), and a measurement of Act would provide a Q2 = 0 baseline for the study of the transition from hard partonic picture to soft Reggeon exchange picture. 2.3 The physics goals in brief The primary physics goal is to determine the afl and aai intercepts (in case N3/2 — N1/2 follows Regge) and thus validate the convergence of the GDH integral. We intend for instance, acquire the data precise enough to result in uncertainties Aaa, = ±0.008, Aafl = ±0.016 as compared to Aaa, = ±0.23, 102 S. Sirca Aaf, = ±0.22 from ELSA: see Fig. 6. The secondary physics goal is to improve the current experimental accuracy of the GDH integral by « 25 % (with reasonable assumptions on APe, APt, and absolute normalization). Finally, regardless of the convergence and sum rule validity, we would be able to explore the region of diffractive QCD relevant to EIC physics. -ss Ü k. Is SJ -ss i e* o, Ü 5J o 3 X2/ndf 200.8 / 178 P1 210.3 P2 -0.6635 - ......................... 9 10 A'Vndf P1 P2 11 12 V (GeV) 177.0 / 178 -17.59 0.4046 4 5 6 7 8 9 10 11 12 V (GeV) Fig. 6. The expected precision of the isoscalar (top panel) and isovector (bottom panel) polarized cross-section differences (plotted on a Regge curve). 3 4 5 6 7 8 References 1. J. E. Amaro, R. Ruiz Arriola, Phys. Rev. D 93, 053002 (2016). 2. J. A. Formaggio, G. P. Zeller, Rev. Mod. Phys. 84,1307 (2012). 3. A. Liesenfeld et al. (A1 Collaboration), Phys. Lett. B 468, 20 (1999). 4. V. Bernard, N. Kaiser, U.-G. Meißner, Phys. Rev. Lett. 69,1877 (1992); see also comment in Phys. Rev. Lett. 72, 2810 (1994). 5. O. Gryniuk, F. Hagelstein, V. Pascalutsa, Phys. Rev. C 94, 034043 (2016). 6. R. Pantforder, Investigations on the Foundation and Possible Modifications of the Gerasimov-Drell-Hearn Sum Rule, arXiv:hep-ph/9805434. 7. M. Vanderhaeghen, private communication. 8. F. Hagelstein, R. Miskimen, V. Pascalutsa, Prog. Part. Nucl. Phys. 88 (2016) 29. Povzetki v slovenščini Elektromagnetna sklopitev pentakvarkov Roelof Bijker in Emmanuel Ortiz-Pacheco Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Ciudad de Mexico, Mexico V tem prispevku razpravljava o elektromagnetni sklopitvi pentakvarkovskih stanj, ki imajo skrito kvantno število čar. To delo so vzpodbudili nedavni eksperimenti v Evropskem centru CERN (kolaboracija LHCb) in tekoči eksperimenti v laboratoriju JLab (ZDA) z namenom, da s fotoprodukcijo potrdijo obstojcarobno nevtralnih pentakvarkovskih stanj . Resonance in deformacije konture Gernot Eichmann CFTP, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal Dajemo zgled, kako izvrednotiti lastnosti resonanc iz integralnih enacb z Loren-tzevo invarianco. V ta namen resimo Bethe-Salpetrovo enacbo in in sipalne enacbe za skalarni model in dolocimo lege resonancnih polov ter fazne premike. Izkaze se, da skalarni model ne da resonancnih polov v kompleksni ravnini, temvec da virtualna stanja na realni osi druge Riemannove ploskve. Mešanje okusov, nevtrinske oscilacije in mase nevtrinov Harald Fritzsch Department für Physik, Universitat München, Theresienstraße 37, D-80333 München, Germany Predstavim masne matrike z vzorcem s stirimi niclami za kvarke in leptone.Trije koti pri mesanju okusov za kvarke so funkcije kvarkovih mas in se dajo izracunati. Rezultati se skladajo z eksperimentalnimi podatki. Za leptone uporabim masne matrike z vzorcem z niclami ter mehanizem "guncnice", da izracunam matricne elemente leptonske mesalne matrike kot funkcije leptonskih mas. Izracunane vrednosti nevtrinskih mas so mi « 1.4 meV, m2 ~ 9 meV, m3 « 51 meV. Razpravljam o breznevtrinskem dvojnem razpadu beta. Efektivna Majoranova masa nevtrinov, ki opisuje dvojni razpad beta, se da izracunati - znasa okrog 5 meV. Sedanja eksperimentalna zgornja meja je 140 meV. 104 Povzetki v slovenščini Pentakvarki kot molekule s skritim čarom: nekaj odprtih vprašanj Marek Karliner School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel Pri detektorju LHCb (CERN, Ženeva) so nedavno poročaki o treh ozkih stanjih pri razpadih bariona A£ -» J/^ pK-, in sicer Pc(4312), Pc(4440) in Pc(4457), ki razpadajo v J/^ p. Torejimajo minimalno vsebino kvarkov cčuud. Dve stanji sta za malenkost pod pragom za IcD* in eno stanje je za malenkost pod pragom za IcD. To močno namiguje na hadronske molekule in neposredno odpira nekaj mamljivih vprasanj, ki iz tega sledijo. Poenoteni pristop k zgradbi lahkih in težkih barionov Hyun-Chul Kim Department of Physics, Inha University, Incheon 22212, Republic of Korea, School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea V tem prispevku podajam pregled nedavnih del o zgradbi lahkih in tezkih bari-onov, osnovanih na kiralnem solitonskem modelu s kvarki. Pregled je namenjen kot kratek vodnik po modelu. Podrobnosti so na voljo v navedeni literaturi. Izboljšana pionska povprečna polja June-Young Kima, Hyun-Chul Kima'b a Department of Physics, Inha University, Incheon 22212, Republic of Korea b School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea V tem prispevku podajava rezultate z izbopanimi pionskimi povprecnimi polji v okviru kiralnega solitonskga modela s kvarki. Raziskujeva ucinke zmanjsanja stevila valencnih kvarkov od Nc do Nc — 1 in Nc — 2 na pionska povprecna polja in razpravljava o njihovih fizicnih implikacijah. 105 Povzetki v slovenščini Odvisnost lastnosti mezona p(770) od mas lahkih in čudnih kvarkov R. Molinaa, J. Ruiz de Elvirab a Departamento de Física Teórica II, Plaza Ciencias, 1, 28040 Madrid, Spain and Institute of Physics of the University of Sao Paulo, Rua do Matao, 1371 -Butanta, Sao Paulo -SP, 05508-090 b Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland Upostevamo analizo nedavnih faznih premikov pri trku nn (I=J=1) ter podatke z racunov na mrezi za razpadno konstanto psevdoskalarnih mezonov na dveh razlicnih trajektorijah, pri katerih je fiksirana bodisi vsota mas kvarkov u, d in s, bodisi masa kvarka s. Iz tega izpeljemo odvisnost parametrov mezona p od mas lahkih in cudnega kvarka in napovemo parametre na kiralnih trajektorijah, ki privzemajo lazje mase, kot je fizicna masa cudnega kvarka. Ugotovimo, da lahko postane masa mezona p lahka vse do 700 MeV, ce vzamemo maso cudnega kvarka nic in fizicne mase pionov. Pri tem je razmerje sklopitev pri kanalih nn in KK enako %/2 na SU(3) simetricni kiralni trajektoriji. Elektromagnetni oblikovni faktorji nukleona, bariona A in hiperonov Willibald Plessas Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria Obravnavamo elektromagnetno zgradbo barionov v okviru poenotenega rela-tivisticnega modela iz konstituentnih kvarkov. Potem ko ponovimo kovariantne elasticne oblikovne faktorje nukleonov vkljucno z njihovo sestavo glede okusov, nadaljujemo po isti poti proti oblikovnim faktorjem barionov A, A, I in H. Izpostavimo znacilne lastnosti elasticnih elektromagnetnih faktorjev barionov, ki pripadajo bodisi oktetnim, bodisi dekupletnim multipletom glede okusa. Eksotična stanja iz teZkih kvarkov Jonathan L. Rosner Enrico Fermi Institute, University of Chicago, 5640 Ellis Avenue, Chicago, IL 60637 Tezki kvarki c in b stabilizirajo eksoticne mezone (qqqq) in barione (qqqqq) . Predstavim delo z M. Karlinerjem o molekulah, ki vsebujejo (cc) in (bb) ; prvi dvojno carobni barion; izospinske razcepe; mase barionov E+c = ccd in Hcc =ccs; zivljenske case; tetrakvarke, ki so stabilni glede na mocni in elektromagnetni razpad; vzbujena stanja Hc; in vzbuditvene energije v valu P. 106 Povzetki v slovenščini Vpliv vmesnih resonanc na sklopitev kvarkov s fotonom Helios Sanchis-Alepuz University of Graz, A-8010 Graz, Austria Predstavimo glavne rezultate nasega članka z leta 2019, v katerem proučujemo učinke vmesnih hadronskih resonanc v interakcijskem jedru kvarka z antikvar-kom na vozlisče kvarka s fotonom. To je prvi korak na dolgi poti do vključitve nevalenčnih prispevkov v Bethe-Salpetrovem pristopu k hadronskim lastnostim. Analiza delnih valov pri podatkih o fotoprodukciji pionov z zahtevo po analiticnosti pri fiksni spremenljivki t J. Stahova'b, H. Osmanoviča, M. Hadzimehmedoviča, R. Omeroviča a University of Tuzla, Fačulty of Natural Sčienčes and Mathematičs, Univerzitetska 4, 75000 Tuzla, Bosna in Hercegovina b European University Kallos Tuzla, Marsala Tita 2A - 2B, Tuzla, Bosna in Hercegovina Predstavimo rezultate analitično omejene analize delnih valov pri fotoproduk-čijskih podatkih za mezon n0. Vhodne podatke smo dobili iz reakčijp(Y,n0)p in n(y, n0)n od praga vse do energije W = 1.95 GeV. Zgradba in prehodi vzbujenih stanj nukleona pri kromodinamiki na mrezi Finn M. Stokesa'b, Waseem Kamleha in Derek B. Leinwebera a Spečial Research Centre for the Subatomič Stručture of Matter, Department of Physičs, University of Adelaide, South Australia 5005, Australia b Juličh Superčomputing Centre, Institute for Advančed Simulation, Forsčhungszentrum Juličh, Juličh D-52425, Germany Nedavno vpeljana variačijska analiza z razvojem po parnosti (PEVA) omogoča ločevanje barionskih lastnih stanjna mrezi pri končni gibalni količini brez primesi z nasprotno parnostjo. Pokazemo, da ta metoda vpelje statistično pomembne popravke pri izvrednotenju elektromagnetnih oblikovnih faktorjev nukleona v osnovnem stanju. Omogoča tudi prvo izvrednotenje elastičnih in prehodnih oblikovnih faktorjev vzbujenih stanjnukleona na mrezi. Predstavimo elektromagnetne elastične oblikovne faktorje in vijačnostne amplitude dveh vzbujenih stanj nukleona z negativno parnostjo. Te rezultati nudijo nazoren vpogled v zgradbo teh stanjin omogočajo povezavo s stanji iz kvarkovega modela v tem energijskem območju. 107 Povzetki v slovenščini Eksotični barioni v modelih Skyrmovega tipa Herbert Weigel Institute for Theoretical Physics, Physics Department, Stellenbosch University, Matieland 7602, South Africa Kiralni solitonski modeli Skyrmovega tipa predvidevajo nizko leZece eksoticne barione s kvantnimi stevili, ki se ne dajo sestaviti s trem kvarki. V tem prispevku razpravljam o lastnostih njihovih partnerjev z drugacnim okusom v nukleonskem kanalu. Novice z eksperimenta Belle: hadronska spektroskopija Marko Bracko Univerza v Mariboru, Smetanova ulica 17, 2000 Maribor in Institut Jozzef Stefan, Jamova cesta 39,1000 Ljubljana V tem prispevku so predstavljeni izbrani novejši rezultati spektroskopije hadronov pri eksperimentu Belle. Meritve so bile opravljene na vzorcu izmerjenih podatkov, ki gajevcasu svojega delovanja-med letoma 1999 in 2010-zbral eksperiment Belle, postavljen ob trkalniku elektronov in pozitronov KEKB, ki je obratoval v laboratoriju KEK v Cukubi na Japonskem. Zaradi velikosti vzorca in kakovosti izmerjenih podatkov lahko raziskovalna skupina Belle se sedaj, ko je od zakljucka delovanja eksperimenta minilo ze skorajdesetletje, objavlja rezultate novih meritev. Izbor opisanih meritev in njihovih rezultatov odraza interese udeležencev delavnice, kjer so bili rezultati predstavljeni. Enigmatična resonanca A(1600) Bojan Golli Pedagoska fakulteta, Univerza v Ljubljani in Institut Jozef Stefan, 1000 Ljubljana, Slovenija Soocimo opisa dveh vzbujenih stanjnukleona, ki imata v kvarkovskem modelu enako strukturo: Roperjevo resonanco N(1440) v parcialnem valu P11 in resonanco A(1600) v parcialnem valu P33. Medtem ko pri prvi resonanci igra pomembno vlogo kvazivezano stanje mezona sigma in nukleona, pa pri drugi resonanci dominira kvazivezano stanje piona in resonancnega stanja A(1232). 108 Povzetki v slovenščini Fenomenološka spodnja meja za maso bariona E+c+ Mitja Rosina Fakulteta za matematiko in fiziko, Univerza v Ljubljani, Jadranska 19, P.O.Box 2964,1001 Ljubljana, Slovenija in Institut Jozef Stefan, 1000 Ljubljana, Slovenija Predstavim preprosto interpolacijo med mezonskimi vezavnimi energijami, ki lahko da dobro semikvantitativno vezavno energijo za dikvark cc in potem se za barion E+c . Masa bariona E+c je zelo malo občutljiva na zelo različne izbire mas konstituentnih kvarkov. Meritev GA in vsotnega pravila GDH pri visokih energijah v centru Jefferson Lab: dva predloga Simon Sirca Fakulteta za matematiko in fiziko, Univerza v Ljubljani, Jadranska 19, P.O.Box 2964,1001 Ljubljana, Slovenija in Institut Jozef Stefan, 1000 Ljubljana, Slovenija Predstavljena sta bila dva eksperimentalna predloga (proposals) za meritvi z elektronskim sipanjem, kjer bi bil center TJNAF (Jefferson Lab) brzkone najprimernejši za njuno izvedbo: modelsko cisto meritev nukleonskega aksialnega oblikovnega faktorja, GA, in meritev visokoenergijskega prispevka k Gerasimov-Drell-Hear-novemu (GDH) vsotnemu pravilu. V obeh primerih je kljucno odstranjevanje elektromagnetnega ozadja, zato poleg optimizacije eksperimentalne postavitve (zlasti polarizirane tarce) ze potekajo podrobne simulacije Monte-Carlo. Blejske Delavnice Iz Fizike, Letnik 20, št. 1, ISSN 1580-4992 Bled Workshops in Physics, Vol. 20, No. 1 Zbornik delavnice 'Elektrošibki procesi pri hadronih', Bled, 15. - 19. julij 2019 Proceedings of the Mini-Workshop 'Electroweak Processes of Hadrons', Bled, July 15 - 19, 2019 Uredili in oblikovali Bojan Golli, Mitja Rosina, Simon ¡Sirca Članki so recenzirani. Recenzijo je opravil uredniski odbor. The articles are peer reviewed by the Editorial Board Izid publikacije je finančno podprla Javna agencija za raziskovalno dejavnost RS iz sredstev drzavnega proracuna iz naslova razpisa za sofinanciranje domacih znanstvenih periodicnih publikacij. Tehnicni urednik Matjaz Zaverenik Zalozilo: DMFA - zaloznistvo, Jadranska 19,1000 Ljubljana, Slovenija Natisnila tiskarna Itagraf v nakladi 70 izvodov Publikacija DMFA stevilka 2104 Brezplacni izvod za udelezence delavnice