Blejske delavnice iz fizike Letnik 19, št. 1 Bled Workshops in Physics Vol. 19, No. 1 ISSN 1580-4992 Proceedings of the Mini-Workshop Double-charm baryons and dimesons Bled, Slovenia, June 17 - 23, 2018 Edited by Bojan Golli Mitja Rosina Simon Sirca University of Ljubljana and Jozef Stefan Institute dmfa - ZALOŽNIŠTVO Ljubljana, november 2018 The Mini-Workshop Double-charm baryons and dimesons 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 Organizing Committee Mitja Rosina, Bojan Golli, Simon Sirca List of participants EefVan Beveren, Coimbra, eef@teor.fis.uc.pt Bojan Golli, Ljubljana, bojan.golli@ijs.si Madanagopalan Padmanath, Regensburg, Padmanath.Madanagopalan@physik.uni-regensburg.de Willi Plessas, Graz, willibald.plessas@uni-graz.at Bogdan Povh, Heidelberg, b.povh@mpi-hd.mpg.de Saša Prelovšek, Ljubljana, sasa.prelovsek@ijs.si Jean-Marc Richard, Lyon, j-m.richard@ipnl.in2p3.fr Mitja Rosina, Ljubljana, mitja.rosina@ijs.si Simon Sirca, Ljubljana, simon.sirca@fmf.uni-lj.si Daniele Treleani, Trieste, daniel@ts.infn.it Electronic edition http://www-f1.ijs.si/BledPub/ Contents Preface............................................................. V Predgovor..........................................................VII Mesonic Spectra: Experimental Data and Their Interpretation E. van Beveren, G. Rupp.............................................. 1 Heavy baryon spectroscopy from lattice QCD M.Padmanath ...................................................... 10 Universal Constituent-Quark Model for All Baryons W.Plessas.......................................................... 18 Doubly-heavy baryons, tetraquarks and related topics J.-M. Richard, A. Valcarce, J. Vijande................................... 24 Production of Pairs of Heavy Quarks by Double Gluon Fusion D. Treleani.......................................................... 32 The Roper resonance as a meson-baryon molecular state B.Golli............................................................. 37 Double charm baryons and dimesons MitjaRosina ........................................................ 41 Pion electroproduction in the energy region of the Roper resonance S. Sirca............................................................. 45 Discussion sessions Workshop participants............................................... 46 Povzetki v slovenscini............................................... 49 Preface This year the Bled Mini-Workshop was devoted to the double-charm hadrons, as the discovery of the double-charm baryon E++ = ccu at LHCb revived the interest for the search of double charm dimesons. The first question is whether the DD* dimeson is bound or is it a low-lying resonance. In models using quark exchange it is only weakly bound; pion exchange might supply extra binding but no reliable model calculation has been performed so far. The second question is what would be a good signature for its detection, since the production and decay processes are not as clear as in the case of E++. We hope that our present discussions and future ideas could give a hint to experimentalists for a search, especially at the upgraded Belle II facility. Both constituent quark models and lattice QCD simulations are helpful and are already giving a lot of insight. They both support the value 3620 MeV for the mass of the E++ baryon found at LHCb. However, the controversial E+ baryon at 3520 MeV (SELEX) is not yet completely excluded as a possible lower state. The mechanism of the dimeson production via a cc diquark is a challenge. The encouragement comes from the copious double cc production seen at Belle. Theoretical explanation is still missing. Nucleon resonances were also a side topic of the meeting, among them mostly the Roper resonance which remains a major challenge in spite of recent developments in lattice QCD. It is broad and hard to see directly in spectra, and it is still unclear to what extent it is a breathing mode of the proton (a three-quark system) or a dynamically generated resonance. Experimentally it has been studied by electroexcitation, and theoretically by coupled-channel analysis (the nN, oN, nA channels, as well as channels with p, and K). The provocative peaks E(38 MeV) and Z(57.5 GeV) also ask for explanation. We would like to thank again all participants for coming and providing new perspectives on the phenomena of our common interest. It is so encouraging that in such a small and friendly group we can tell each other the strong and the weak points of our approaches and profit from the frank criticism and suggestions. We shall do our best that these popular Mini-Workshops continue every year and we hope to see you at Bled again. Ljubljana, November 2018 B. Golli, M. Rosina, S. Sirca P. S.: Several figures and diagrams originally presented in colour are reproduced here in grayscale, whereby some information is lost. The color version is available at http://www-f1.ijs.si/BledPub. Predgovor Letos je bila blejska delavnica posvečena dvojno čarobnim hadronom, sajje odkritje dvojno čarobnega bariona E++ = ccu na pospesevalniku LHCb oživilo zanimanje za iskanje dvojno čarobnih dimezonov. Prvo vprasanje je, ali je dimezon DD* vezan, ali je nizko lezeča resonanca. Ce upostevamo izmenjavo kvarkov, je samo sibko vezan; izmenjava pionov lahko dodatno veze, toda doslejse ni zanesljivega računa. Drugo vprasanje je, kako bi ga prepoznali, kajti tvorba in razpad nista tako značilna kot pri barionu E++. Upamo, da bodo nasa sedanja razmisljanja in bodoče ideje pomagale eksperimentalcem pri iskanju, zlasti na povečanem detektorju Belle II. Dosti vpogleda dobimo od računov s kvarkovimi modeli kakor tudi od simulacije kromodinamike na mrezi. Oboje je v skladu z maso bariona E++ 3620 MeV, ki so jo izmerili na pospesevalniku LHCb. Toda sporna masa bariona E+ okrog 3520 MeV pri detektorju SELEX se ni čisto izključena kot mozno najnizje stanje. Izziv je tudi produkcija dimezonov preko dikvarka cc. Vzpodbudo daje obilna produkcija dvojnih parov cč, ki so jo izmerili na detektorju Belle. Teoretična razlaga se manjka. Kot stransko temo srečanja smo obravnavali tudi nukleonske resonance, zlasti Roperjevo resonanco, ki predstavlja se vedno velik izziv kljub nedavnemu napredku pri kromodinamiki na mrezi. Resonanca je siroka in jo je tezko opaziti v v spektrih; se vedno je nejasno, do koliksne mere je sistem treh kvarkov ("dihanje" protona) ali dinamično povzročena resonanca. Eksperimentalno so jo preučevali z vzbujanjem z elektroni, teoretično pa z analizo sklopljenih kanalov ( nN, oN, nA), tudi takih z mezoni p, in K. Izzivalna vrhova pri 38 MeV in pri 57,5 GeV tudi kličeta k preverjanju in razlagi. Radi bi se zahvalili vsem udeležencem, da so se udelezili srečanja in nudili nove perspektive pri pojavih, ki nas vse zanimajo. Vzpodbudno je, da si lahko v taksni majhni in prijateljski skupini povemo tako močne kot sibke točke pri nasih pristopih in nam koristijo odkrita kritika in namigi. Potrudili se bomo, da se bo ta priljubljena Delavnica nadaljevala vsako leto in upamo, da se spet vidimo na Bledu. Ljubljana, november 2018 B. Golli, M. Rosina, S. Sirca P. S. Marsikatere slike in diagrame smo prejeli v barvah, toda v tiskanem Zborniku so sivi, s čimer se zgubi nekajinformacije. Barvno verzijo lahko dobite na http://www-f1.ijs.si/BledPub. 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 24-30, 2018), Vol. 19 (2018) 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 Bled Workshops in Physics Vol. 19, No. 1 p.l Mesonic Spectra: Experimental Data and Their Interpretation* E. van Beverena, G. Ruppb a Centro de Física da Universidade de Coimbra, Departamento de Física, Universidade de Coimbra, P-3004-516 Coimbra, Portugal b Centro de Física e Engenharia de Materiais Avancados, Instituto Superior Tecnico, Universidade de Lisboa, P-1049-001 Lisboa, Portugal Abstract. We discuss experimental data and their interpretation. In particular, we argue that spectra of quark-antiquark systems should better be studied from configurations with well-defined quantum numbers, the most suitable system being charmonium. We suggest probable future findings based on the existing low-statistics data for charmonium and bottomonium. We also briefly review our findings for the E(38 MeV) and Z(57.5 GeV) bosons. Observation and its interpretation are human activities not restricted to a handful of experts but open to anyone who feels the need to express an opinion. A nice example of the importance of observation is the meticulous registration of atomic and molecular line spectra during the nineteenth and the twentieth century. Moreover, its history of interpretation shows exemplarily the struggle of the human mind to escape from prevailing standard models. It starts with the color-separation theory of Wollaston, based on his pioneering observation in the early 1800s of seven dark lines in the solar spectrum. Decades later that interpretation was proven to be wrong by Kirchhoff and Bunsen, based on the observation of emission spectra. Thomson's plum-pudding model in the early 1900s, shortly after the discovery of electrons, was the last attempt to keep observation within accepted theories. Finally, Bohr's proposal gave the breakthrough for a solid description of line spectra and the emergence of a new standard model. A century full of observation, improving equipment and new discoveries had passed in order to figure it out. The history of atomic and molecular line spectra resembles that of mesonic spectra. But it fails when it comes to high-quality data. Bohr's model could be tested on a wealth of experimental results. Models for mesonic resonances do not have such luxury at their disposal, which has culminated in a plethora of * Talk presented by E. van Beveren Fig. 1. The 1P beautonium states. Top: ARGUS data (DESY, 1985). Bottom: ATLAS data (CERN, 2011). speculations. Though one wishes that future experiments will improve on statistics, the reality is quite different, as is most strikingly exhibited in Fig. 1, where three-decades-old data [1] on bb —» Yy are compared to more recent results [2]. In this short paper we will highlight some of our somewhat speculative suggestions about the interpretation of mesonic spectra based on observation but not yet confirmed by dedicated experiments. Fig. 2. The D*D* mass distribution measured and published by the BABAR Collaboration. At several occasions we have pointed out the indispensable need for high-statistics data on two-particle mass distributions. As an example may serve the data shown in Fig. 2, where we represent a D*D* mass distribution measured and published by the BABAR Collaboration [3]. At first sight these data do not give us further information on the cc vector-meson spectrum. Indeed, a bin size of 25 MeV is clearly too large for the narrow dominantly-D states and even for the somewhat broader dominantly-S states, whereas also the number of events is barely enough to show an enhancement of the ^(4040). However, one must bear in mind the following. In the first place, the reconstruction of a pair of D* mesons out of kaons, pions and photons is a far from trivial task. The procedure is indicated in Ref. [3]. But it is not clear to us what fraction of produced D*D* pairs is recognized that way. We assume that it is a relatively small fraction. Next, we know from theory that the higher the cc vector meson mass, the smaller its coupling to D*D*. The reason is that, under the assumption of 3Po quark-pair creation, the number of possible two-meson configurations to which a cc vector meson couples grows rapidly with radial excitation [4]. Consequently, the coupling to a specific channel, in the present case D*D*, diminishes substantially for higher radial excitations, thus leading to decreasing enhancements. Finally, S- and D-wave cc vector states mix, which implies that pure S- or D-wave states do not exist in nature. But mixing also has two other interesting consequences. Namely, the dominantly D-wave states almost decouple from meson-pair production, leading to narrow resonances and small mass shifts, whereas the relatively broad S-wave states can easily dominate in decay and so confound their classification. The second consequence of mixing is that the dominantly S-wave states couple more strongly to meson.pair production than expected for pure S-wave states, giving rise to larger widths and considerable mass shifts [5]. So the question comes up why, in the absence of good data, we insist on dealing with cc vector mesons. The answer to that question rests in our belief that these mesons form the backbone of quark-antiquark q q spectra: 1. In the process e-e+ —» D*D*, vector-meson dominance ensures the production of cc vector states. Hence, there is no confusion with different quantum numbers. 2. Little to no influence is expected from non-strange, strange and bottom qq pairs. Consequently, when we know the full details of the cc vector spectrum, we can easily fill up the gaps for the remaining configurations and then use that for the analyses of different flavor combinations. In Fig. 3 we have depicted the poor data for the D*D* mass distribution, together with a comparison to our predictions [6]. The crosses on the horizontal axis indicate the masses of bare cc vector states, i.e., the spectrum in the absence of two-meson configurations, where in our model [5] S- and D-states are degenerate. By allowing cc to couple to open-charm configurations, the predicted dominantly-D states shift only a few MeV, whereas the mass shifts for the domi-nantly-S states are of the order of 100-300 MeV. The enhancement indicated by AcAc is explained in Ref. [7] (see also Fig. 4). Given the importance of the cc vector states for meson spectroscopy, it escapes us why after four decades high-statistics data still do not exist. But maybe Fig. 5 explains it. In the following we will make some suggestions about the bb vector spectrum, as well as the E(38 MeV) and Z(57.5 GeV) bosons. Fig.3. The poor data for the D*D* mass distribution together with a comparison to our predictions. Fig. 4. ^(5S) and ^(4D) besides the large signal (Y(4660)) at the Ac Ac threshold. In Fig. 6 we show our result for the Y(2D) bb vector state at about 10.5 GeV, some 70 MeV below the BB threshold. The data are taken from Ref. [8], while our analysis is discussed in Ref. [9]. A bound state as close to threshold as the Y(2D) is supposed to have a large influence on the threshold enhancement. In Fig. 7 we have depicted Rb-ratio data from Ref. [10], in which one indeed observes a large threshold enhancement peaking at about 10.58 GeV, followed by two more modest enhancements above the BB * and B*B* thresholds. The figure also shows that the former enhancement is listed under Y(4S) in Ref. [11] and, moreover, that our model does not agree with that assignment. This is substantiated in Fig. 8, where TE stands for threshold enhancement, BW for Breit-Wigner line shape. In view of the above discussion on the decrease of resonance enhancements, it seems to us quite reasonable that the Y(4S) is a modestly peaked structure. Moreover, its central mass at about 10.73 GeV agrees better with our model predictions. Fig. 5. The 2009 cc vector spectrum. EXP: PDG + new states; RSE: PRD 21, (1980); FUNNEL: representative for MOST other models; LQCD: representative for lattice QCD. Fig. 6. Our result for the Y(2D) bb vector state at about 10.5 GeV, some 70 MeV below the BB threshold. The discovery of the E(38) boson [12] is discussed in the web version of the talk [13] (click start, then E38, and check the slides from r0 to compass2). The slides r0 and p 0 show why we expected a quantum of about 30-40 MeV, to be associated with quark-pair creation, already since the 1980s. Hints from experimental results came later as exhibited in slides from wobbles to more. More promising data [14,15] are shown in slides from yy to compass2. However, the COMPASS Collaboration contested our proposal by claiming that the enhancement at about 38 MeV is due to an artifact, the details of which are explained in Ref. [16]. Now it must be mentioned that the COMPASS Collaboration has done excellent work on light-meson spectroscopy [17]. Unfortunately, in the effort to substantiate the artifact claim, the COMPASS Collaboration compared apples and BB BB* B*B* BSBS 1.5- Rb 1.0 0.5 PDG • T(4S) * \H ORSE • • 10.60 10.65 10.70 10.75 M(e"e+) (GeV) Fig. 7. The Rb -ratio data from Ref. [10] with a large threshold enhancement peaking at about 10.58 GeV, followed by two more modest enhancements above the BIB * and B*B * thresholds. M(e"e+) (GeV) Mc-c+ (GeV) Fig. 8. Left: detail enhancements. Right: threshold enhancements and resonances. oranges by referring to the low-statistics data of Ref. [14] instead of to the high-statistics data of Ref. [15]. But even the Monte-Carlo simulation for the former data do not minimally confirm their explanation, as shown in Fig. 9. We are still awaiting the follow-up on Ref. [18], which tentatively confirmed the existence of the E(38) [19]. For our suggestion of the existence of a boson at about 57.5 GeV, we only see some hints in experimental data. In Fig. 10 [20] we observe a rather sharp dip in the amplitude at about 115 GeV. When we sift through other observations in that energy region from the CMS, ATLAS and LEP Collaborations and combine the data [20-23] in Fig. 14, we find some indications of agreement. Now, such a sharp minimum in the data could indicate the onset of a threshold enhancement, moreover inflated due to the presence of a resonance at about 125 GeV, and most probably resulting from the creation of a pseudoscalar (or scalar) boson pair of half the onset mass each The L3 Collaboration might have searched for such a boson in Z —» yyy [24]. But with a total of 87 events not much statistics can be expected, as we see in Figs. 11 and 12. Nevertheless, a small effect is visible Fig. 9. Diphoton Monte-Carlo simulation from the COMPASS Collaboration compared to the data. Fig. 10. Diphoton data from the CMS Collaboration. Fig. 11. Z —> Zy —> yyy. Solid line: QED expectation. The shaded area represents the expected one-photon energy for M(Z) = 57.5 GeV. Fig. 12. Data divided by QED. The excess is where expected for Z of 57.5 GeV. Fig. 13. Diphoton data from the CMS Collaboration compared to Standard-Model predictions DIPHOX (left) and RESBOS (right). Fig. 14. Other LHC and LEP data agree. Shown are the data for CMS yy, ATLAS yy, CMS 4 leptons, ATLAS 4 leptons, L3 e+e- -> t+t-(y) and L3 e+e- -> m+mT(y). precisely where expected. Further indications come from comparison of diphoton data from the CMS Collaboration with predictions of DIPHOX and RESBOS [25], shown in Fig. 13. It should not be too difficult to obtain clean data at LHC to improve the Z —> 3y statistics. Acknowledgment One of us (EvB) wishes to thank the organizers of the Mini-Workshop Bled 2018 on "Double-charm baryons and dimesons" for their hospitality. References 1. H. Albrecht et al. [ARGUS Collaboration], Phys. Lett. B 160, 331 (1985). 2. G. Aad et al. [ATLAS Collaboration], Phys. Rev. Lett. 108,152001 (2012) [arXiv:1112.5154]. 3. B. Aubert [BaBar Collaboration], Phys. Rev. D 79, 092001 (2009) [arXiv:0903.1597]. 4. E. van Beveren, Z. Phys. C 21, 291 (1984) [arXiv:hep-ph/0602246]. 5. E. van Beveren, C. Dullemond and G. Rupp, Phys. Rev. D 21, 772 (1980) [Erratum-ibid. D 22,787(1980)]. 6. E. van Beveren and G. Rupp, Chin. Phys. C 35, 319 (2011) [arXiv:1004.4368]. 7. E. van Beveren and G. Rupp, Phys. Rev. D 80, 074001 (2009) [arXiv:0908.0242]. 8. B. Aubert et al. [BaBar Collaboration], Phys. Rev. D 78,112002 (2008) [arXiv:0807.2014]. 9. E. van Beveren and G. Rupp, arXiv:1009.4097. 10. B. Aubert [BaBar Collaboration], Phys. Rev. Lett. 102, 012001 (2009) [arXiv:0809.4120]. 11. M. Tanabashi et al. [Particle Data Group Collaboration], Phys. Rev. D 98, 030001 (2018). 12. E. van Beveren and G. Rupp, arXiv:1202.1739. 13. http://cft.fis.uc.pt/eef/bled2018start.htm 14. J. Bernhard and K. Schonning [COMPASS Collaboration], eConf C110613,146 (2011) [arXiv:1109.0272]. 15. T. Schlüter [COMPASS Collaboration], eConf C110613, 302 (2011) [arXiv:1108.6191]. 16. J. Bernhard, J. M. Friedrich, T. Schlüter, K. Schonning [COMPASS Collaboration], arXiv:1204.2349. 17. S. Wallner [COMPASS Collaboration], PoS Hadron 2017, 032 (2018), [arXiv:1711.09782]. 18. Kh. U. Abraamyan, A. B. Anisimov, M. I. Baznat, K. K. Gudima, M. A. Nazarenko, S. G. Reznikov and A. S. Sorin, arXiv:1208.3829. 19. Private communication with A. S. Sorin at the 8th International Workshop "Excited QCD", 6-12 March 2016, Costa de Caparica, Portugal. 20. [CMS Collaboration], CMS-PAS-HIG-13-016. 21. S. Chatrchyan et al. [ CMS Collaboration], Phys. Rev. D 89, 092007 (2014) [arXiv:1312.5353]. 22. S. M. Consonni [for the ATLAS Collaboration], Report ATL-PHYS-PROC-2013-114 [arXiv:1305.3315]. 23. M. Acciarri et al. [L3 Collaboration], Phys. Lett. B 479, 101 (2000) [arXiv:hep-ex/0002034]. 24. M. Acciarri et al. [L3 Collaboration], Phys. Lett. B 345, 609 (1995). 25. [CMS Collaboration], CMS-PAS-HIG-13-001, March 21 (2013). Bled Workshops in Physics Vol. 19, No. 1 p. 10 Heavy baryon spectroscopy from lattice QCD M. Padmanath Institüt für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Abstract. In this report, the most recent and precise estimates of masses of ground state baryons using lattice QCD are discussed. Considering the prospects in the heavy baryon sector, lattice estimates for these are emphasized. The first and only existing lattice determination of the highly excited Oc excitations in relation to the recent LHCb discovery is also discussed. 1 Introduction Since its inception, heavy hadron physics continues to be in the limelight of scientific interests in understanding the nature of strong interactions. While heavy mesons have been studied extensively both experimentally and theoretically [13], studies on heavy baryons remained dormant. In this respect, the year 2017 featured two important landmarks in the heavy baryon physics. First of this is the unambiguous observation by LHCb collaboration of five new narrow D.c resonances in E+K- invariant mass distribution in the energy range between 3000 — 3120 MeV [4]. Four out of these five resonances were later confirmed by Belle collaboration [5]. Second landmark is the discovery of a doubly charmed baryon, E+c(ccu) with a mass of 3621.40 ± 0.78 MeV by LHCb Collaboration [6]. Anticipating the discovery of many more hadrons (including baryons) from the huge data being collected at LHCb and Belle II, heavy hadron spectroscopy using ab-initio first principles methodology such as lattice QCD is of great importance. Lattice QCD has been proven to be a novel non-perturbative technology in investigating the physics of low energy regime of QCD. Remarkable progress has been achieved over past ten years in making large volume simulations with physical quark masses, impressive statistical precision and good control over the systematic uncertainties [7-10]. In this report, a collection of lattice determinations of baryon masses that are well below allowed strong decay thresholds are summarized. A recent and only existing calculation of excited Hc baryons is discussed and a qualitative comparison with the experiment is made. 2 Lattice methodology Hadron spectroscopy on the lattice proceeds through evaluation of Euclidean two point correlation functions, between different hadronic currents (Oi(t)) that are carefully built to respect the quantum numbers of interest. A generic baryon current or interpolator has a structure Oi (x,t) = eabcSf6(x)qa,a(x)qb,p(x)q3,6(x), (2) where qj are the quark fields, e is the color space anti-symmetrizing Levi-Civita tensor and S carries all the flavor and spatial structure of the interpolator that determines the quantum information. Cij(tf — ti) are evaluated on lattice QCD ensembles that are generated via Monte Carlo techniques. A general practice is to compute matrices of correlation functions between a basis of carefully constructed interpolating currents Oi(t) and solving the generalized eigenvalue problem (GEVP) [11-13] Cij (t) vn (t — to) = An (t — to) Cij (to )vn (t — to). (3) Hadron energies (En) are extracted from non-linear fits to the large time behavior of the eigenvalues An(t — t0). The eigenvectors (vn(t — t0)) are related to the operator state overlaps (Zn = (Oi|n)) that carry the quantum information of the propagating state. Basic principles remain the same as above, while details of the methodology differ between different groups in the lattice community. e.g. lattice ensembles being used in the study, lattice formulation of action for the fermion and the gauge fields, the hadron interpolators, different degree of control over the lattice systematics, etc. The success of lattice investigations are reflected in mutual agreement of the results they provide and their agreement with experiments. All results presented in this report are estimated within the single hadron approximation, where only three quark interpolators (as in eqn. 2) are considered in the analysis and neglects effects of any nearby strong decay thresholds. This is a justifying assumption for most of the baryons discussed in this report, considering the fact that all of them are deeply below the respective lowest strong decay thresholds. Results for those baryons, which might be influenced by any nearby threshold effects will be alerted in the respective discussions. 3 Results Light, strange and singly charm baryons : We begin our discussion with some benchmark calculations of baryon ground states that are experimentally well determined. In Fig. 1, a summary of lattice QCD estimates for the positive parity light baryon ground states (figure adapted from Ref. [10]) are presented at the top and for positive parity singly charm baryon ground states are shown at the bottom. Most of the baryons being discussed are deeply bound and stable to strong decays. Their masses as determined from the discrete energy spectrum on the lattice agree quite well with experiments. Agreement between all the lattice estimates with varying degree of control over the systematics involved in respective calculations and with the experiments demonstrate the power of lattice QCD techniques in making reliable predictions. However, lattice estimates for masses of baryon resonances, such as A, I* and E* that can decay strongly, are less rigorous. They demand a computation of correlation matrices build out of baryon 1.8 1.7 1.6 1.5 1.4 1.3 1.2 I.I 1 0.9 ETMC Nf -2 ET MC N, = 2 + 1 + 1 QCDSF-UKQCD N, = 2+1 PACS-CS N, = 2+1 bmw N, = 2+1 IT^1"' ik N H A n 2800 d) s ' 2600 — : Expt '17 t : HSC 15 I : ILGTI'13-'18 1 : Brown et.al. '14 1 : TWQCD '17 t : PACS-CS '13 + : ETMC '17 t : Briceno et.al. '12 + : RQCD'15 : Durretal. '12 4 V* Ac Zc Zc* Sc 77/ Oc o; Fig. 1. Top: summary of lattice estimates for positive parity light and strange baryons from selected lattice investigations - ETMC Nf=2 [10], ETMC Nf=2+1+1 [14], QCDSF-UKQCD Nf=2+1 [15], PACS-CS Nf=2+1 [8] and BMW Nf=2+1 [7], Bottom: summary of lattice estimates for positive parity singly charm baryons : ILGTI '13-'18 [16,17], TWQCD '17 [18], ETMC '17 [10], RQCD '15 [19], HSC '15 [20,21], Brown et nl '14 [22], PACS-CS '13 [8], Briceno et nl '12 [23], Dürr et nl '12 [24], interpolators (as in eqn. 2) plus baryon-meson interpolators (corresponding to the allowed strong decay modes). The masses of baryon resonances then have to be inferred from the infinite volume scattering matrices build from the discrete spectrum extracted from such correlation matrices. Such investigations are being practised extensively by many collaborations to understand various mesonic resonances (see Ref. [3]), while existing lattice investigations of baryon resonances in this direction are limited to a few [25,26]. Doubly heavy baryons : In Fig. 2, a summary of lattice QCD estimates for positive parity doubly charm baryon ground states at the top is presented. For the Ecc(1 /2+) baryon, good agreement between all lattice estimates (all of which predates the LHCb-discovery [6]) and with LHCb estimate is quite evident from the figure. At this point, the reader is reminded of the observation of another baryon resonance by SELEX collaboration in 2002 [27] at a mass of 3519(1) MeV, S O Expt '17 ILGTI '13 - '18 TWQCD '17 ETMC '17 RQCD '15 HSC '15 Brown et.al. '14 PACS-CS '13 Briceno et.al. '12 Durr et al. '12 I "'I TT* —cc Qc G AS —♦— A5 •— — experiment • QCD+QED ■j prediction AD —♦— AN Fig. 2. Top: summary of lattice estimates for positive parity doubly charm baryons. References as given in Fig. 1 caption. Bottom: Hadron isospin splittings as determined by BMW collaboration [9]. which is addressed as a Ecc(l /2+) baryon. All lattice estimates, being well above this energy, disfavors this observation. The bottom figure shows a summary of baryon isospin splittings as calculated by BMW collaboration [9]. This calculation involved lattice QCD and QED computations with four non-degenerate fermion flavors to estimate the isospin mass splitting in the nucléon, I, E, D and Ecc isospin multiplets. Precise estimation of the neutron-proton isospin splitting and the other known splittings demonstrate the reliability of these estimates. In this calculation, the isospin splitting of Ecc(l/2+) baryon was estimated to be 2.16(11)(17) MeV. This excludes the possibility that LHCb and SELEX candidates for Ecc(l/2+) baryon are isospin partners. Estimates for other doubly charm baryons, that are yet to be discovered, can also be observed to be very well determined and consistent between different lattice calculations from the top of Fig. 2. Anticipating a near future discovery of the charmed-bottom hadrons at LHCb, at the top of Fig. 3 lattice predictions for such hadrons from a recent investigation [28] are shown. The lattice prediction for only know charmed-bottom hadron, Bc meson, is found to be in agreement with the experiment, while the lattice predictions for other channels considered are consistent with another preceding calculation [22] with less control over systematics. 0.4 0.3 0.1 ac h 3/2* 1/2* Expt. Lattice 3/2~ S, K (S) Fig. 3. Top: summary of lattice estimates for low lying charmed-bottom hadrons as determined in Ref. [28]. Bottom: Comparison plot from Ref. [32] between the lattice estimates and the experimental values for the energies of Oc excitations. SK Excited baryons : As discussed in the introduction, one of the major landmark in the year 2017 is the LHCb discovery of five narrow Hc resonances in E+K-invariant mass distribution in the energy range between 3000 — 3120 MeV [4]. Following this discovery, Belle collaboration has confirmed four out of these five excited states [5]. Many more highly excited baryons are coming into light with more discoveries. e.g. the observation of a H*-(3/2-) candidate with a mass of 2012.4(9) MeV by Belle collaboration [29], which is in very good agreement with lattice prediction for such a baryon [30,31]. Below we discuss the first and only existing lattice investigation of highly excited Hc resonances (Ref. [32]) that predicts the five excited D.c baryons as observed by LHCb. Following a detailed baryon interpolator construction procedure as invented in Ref. [33,34] a large basis of baryon interpolators, that is expected to extensively scan the radial as well as orbital excitations, are built. By solving the GEVP for correlation matrices constructed out of these interpolators on a lattice ensemble with mn ~ 391 MeV (for details see [21]), one extract the Hc baryon spectrum on the lattice. The bottom of Fig. 3 shows a comparison of the lattice energy estimates for the lowest nine Hc excitations with the seven experimentally observed nc resonances. The relevant strong decay thresholds in the infinite volume are shown as black lines at the top, whereas the black lines at the bottom indicate the relevant non-interacting levels on the lattice. The lowest two levels represent the well known 1/2+ and 3/2+ excitations. Lattice estimates for these excitations agree well with the experiment. In the energy region, where the five narrow resonances were observed, lattice predicts exactly five levels. Of these five excitations four are in good agreement with the experiment, while the fifth is possibly a 5/2-baryon related to the remaining higher lying experimental candidate. Identifying the quantum information of these lattice levels from the Z^s, these five states are argued to be the p-wave excitations [32]. Considering the exploratory nature of this first study, investigating Hc baryon spectrum on multiple lattice ensembles with close to physical mn and larger volumes would be an immediate extension. It would also be an interesting direction to extract the infinite volume scattering matrices considering the allowed baryonmeson scattering channels in the analysis of desired quantum channels in appropriate lattice ensembles. However, the presence of a valence heavy quark, the absence of any valence light quarks and the resonance widths being quite narrow (< 10 MeV) [6] indicates our estimates to be robust with such extensive investigations. 4 Summary Over the past decade, lattice QCD has availed multiple precision determinations of the ground state baryon masses using full QCD lattice ensembles with good control over the systematic uncertainties. A summary of lattice determinations of various baryons along with their masses from experiment, where available, are given in Figs. 1, 2 and 3. The only existing exploratory lattice determination of the highly excited D.c states in relation to the recent LHCb discovery and its possible extensions are also discussed. 5 Acknowledgements I would like to thank my collaborators N. Mathur, R. G. Edwards, M. J. Peardon and S. Mondal. I also express my thanks to the organizers and the participants of the Bled workshop for various interesting and insightful discussions. I acknowledge the support from EU under grant no. MSCA-IF-EF-ST-744659 (XQCD-Baryons) and Deutsche Forschungsgemeinschaft Grant No. SFB/TRR 55. References 1. N. Brambilla et a/., Eur. Phys. J. C 74, no. 10, 2981 (2014) doi:10.1140/epjc/s10052-014-2981-5 [arXiv:1404.3723 [hep-ph]]. 2. S. L. Olsen, PoS Bormio 050 (2015) [arXiv:1511.01589 [hep-ex]]. 3. S. Prelovsek, EPJ Web Conf. 129, 00018 (2016) [arXiv:1609.03052 [hep-ph]]. 4. R. Aaij et a/. [LHCb Collaboration], Phys. Rev. Lett. 118, no. 18, 182001 (2017) [arXiv:1703.04639 [hep-ex]]. 5. J. Yelton et a/. [Belle Collaboration], Phys. Rev. D 97, no. 5, 051102 (2018) [arXiv:1711.07927 [hep-ex]]. 6. R. Aaij et a/. [LHCb Collaboration], Phys. Rev. Lett. 119, no. 11, 112001 (2017) [arXiv:1707.01621 [hep-ex]]. 7. S. Durr et a/., Science 322,1224 (2008) [arXiv:0906.3599 [hep-lat]]. 8. Y. Namekawa et a/. [PACS-CS Collaboration], Phys. Rev. D 87, no. 9, 094512 (2013) [arXiv:1301.4743 [hep-lat]]. 9. S. Borsanyi et a/., Science 347,1452 (2015) [arXiv:1406.4088 [hep-lat]]. 10. C. Alexandrou and C. Kallidonis, Phys. Rev. D 96, no. 3, 034511 (2017) doi:10.1103/PhysRevD.96.034511 [arXiv:1704.02647 [hep-lat]]. 11. C. Michael, Nucl. Phys. B 259, 58 (1985). doi:10.1016/0550-3213(85)90297-4 12. M. Luscher, Commun. Math. Phys. 104,177 (1986). doi:10.1007/BF01211589 13. B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, JHEP 0904, 094 (2009) doi:10.1088/1126-6708/2009/04/094 [arXiv:0902.1265 [hep-lat]]. 14. C. Alexandrou, V. Drach, K. Jansen, C. Kallidonis and G. Koutsou, Phys. Rev. D 90, no. 7,074501 (2014) [arXiv:1406.4310 [hep-lat]]. 15. W. Bietenholz et a/., Phys. Rev. D 84, 054509 (2011) doi:10.1103/PhysRevD.84.054509 [arXiv:1102.5300 [hep-lat]]. 16. S. Basak, S. Datta, M. Padmanath, P. Majumdar and N. Mathur, PoS LATTICE 2012, 141 (2012) [arXiv:1211.6277 [hep-lat]]. 17. N. Mathur and M. Padmanath, arXiv:1807.00174 [hep-lat]. 18. Y. C. Chen et a/. [TWQCD Collaboration], Phys. Lett. B 767, 193 (2017) doi:10.1016/j.physletb.2017.01.068 [arXiv:1701.02581 [hep-lat]]. 19. P. Perez-Rubio, S. Collins and G. S. Bali, Phys. Rev. D 92, no. 3, 034504 (2015) [arXiv:1503.08440 [hep-lat]]. 20. M. Padmanath and N. Mathur, Charm 2015, arXiv:1508.07168 [hep-lat]. 21. M. Padmanath, R. G. Edwards, N. Mathur and M. Peardon, Phys. Rev. D 91, no. 9, 094502 (2015) [arXiv:1502.01845 [hep-lat]]. 22. Z. S. Brown, W. Detmold, S. Meinel and K. Orginos, Phys. Rev. D 90, no. 9, 094507 (2014) [arXiv:1409.0497 [hep-lat]]. 23. R. A. Briceno, H. W. Lin and D. R. Bolton, Phys. Rev. D 86, 094504 (2012) [arXiv:1207.3536 [hep-lat]]. 24. S. Durr, G. Koutsou and T. Lippert, Phys. Rev. D 86, 114514 (2012) [arXiv:1208.6270 [hep-lat]]. 25. C. B. Lang, L. Leskovec, M. Padmanath and S. Prelovsek, Phys. Rev. D 95, no. 1,014510 (2017) [arXiv:1610.01422 [hep-lat]]. 26. C. W. Andersen, J. Bulava, B. Horz and C. Morningstar, Phys. Rev. D 97, no. 1, 014506 (2018) [arXiv:1710.01557 [hep-lat]]. 27. M. Mattson et a/. [SELEX Collaboration], Phys. Rev. Lett. 89, 112001 (2002) [hep-ex/0208014]. 28. N. Mathur, M. Padmanath and S. Mondal, arXiv:1806.04151 [hep-lat]. 29. J. Yelton et a/. [Belle Collaboration], Phys. Rev. Lett. 121, no. 5, 052003 (2018) [arXiv:1805.09384 [hep-ex]]. 30. R. G. Edwards et al. [Hadron Spectrum Collaboration], Phys. Rev. D 87, no. 5, 054506 (2013) doi:10.1103/PhysRevD.87.054506 [arXiv:1212.5236 [hep-ph]]. 31. G. P. Engel et al. [BGR Collaboration], Phys. Rev. D 87, no. 7, 074504 (2013) [arXiv:1301.4318 [hep-lat]]. 32. M. Padmanath and N. Mathur, Phys. Rev. Lett. 119, no. 4, 042001 (2017) [arXiv:1704.00259 [hep-ph]]. 33. S. Basak et al. [Lattice Hadron Physics (LHPC) Collaboration], Phys. Rev. D 72, 074501 (2005) [hep-lat/0508018]. 34. R. G. Edwards, J. J. Dudek, D. G. Richards and S. J. Wallace, Phys. Rev. D 84, 074508 (2011) [arXiv:1104.5152 [hep-ph]]. Bled Workshops in Physics Vol. 19, No. 1 p. 18 Universal Constituent-Quark Model for All Baryons W. Plessas Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria Abstract. We discuss the performance of a relativistic constituent-quark model that has been constructed in order to provide a universal framework for the description of all known baryons. After recalling some decisive properties of light-flavor baryons we concentrate on the spectroscopy of baryons containing charm and beauty. It has become quite evident that modern constituent-quark models serve as an effective tool for accessing quantum chromodynamics (QCD) at low energies. Essential prerequisites are the observations of Poincare invariance and the spontaneous breaking of chiral symmetry (SBxS). A model constructed in this spirit has been presented now already 20 years ago [1,2]. It assumes constituent quarks with dynamical masses in a linear confinement according to the string tension of QCD and a hyperfine interaction deriving from Goldstone-boson exchange (GBE), where the latter is cast into pseudoscalar meson exchange. The original version covered all baryons with u, d, and s flavors. Their spectroscopy is well described in agreement with phenomenology, yielding in particular the inverse level orderings of the first positive- and negative-parity excitations of the nucleon (N), the JP = 2+ Roper resonance N(1440) and the JP = 2- N(1535), respectively. By solving the eigenvalue problem of the pertinent relativistically invariant mass operator one has beyond the eigenvalues (baryon masses) also access to the wave functions of the baryons. Thereby their structures can be tested as revealed under electromagnetic, weak, strong, and gravitational interactions. All of these types of investigations have been carried out with respect to the N over the past. The elastic N electromagnetic form factors calculated in point form - strictly observing Poincare invariance - have immediately been found in good agreement with experimental data for momentum transfers up to Q2 ~ 4 GeV2 [3,4]. Even the detailed phenomenological insights into the flavor contents of the N electromagnetic form factors are explained correctly, advocating only {QQQ} degrees of freedom [5,6]. Similarly, the covariant axial and induced pseudoscalar N form factors have been described in accordance with phenomenology [7,8]. By the same constituent-quark model a microscopic explanation of the strong nNN and nNA vertex form factors has been provided on the quark level [9]. It largely justifies the phenomeno-logical parameterizations traditionally employed in dynamical models on the hadronic level. Finally the gravitational form factor A(Q2) of the N has been studied yielding results in accordance with other QCD models, see, e.g., Ref. [10]. This kind of structure studies have also been extended to baryon states other than the N, namely to all of the octet and decuplet baryon ground and some of the resonant states. Of course, in these cases comparisons to experimental data are possible only in a few cases, e.g., for electric radii and magnetic moments [4]. In general, very reasonable results have been found, largely also in good agreement with modern lattice-QCD calculations [11-14]. In view of these results it has come up as an interesting question, if the dynamics of GBE can also be extended to all quark flavors, i.e. all baryon states observed so far. This problem has been answered satisfactorily by the universal relativistic constituent-quark model (URCQM) [10,15,16]. It was constructed in the same spirit as its antecessor, the GBE relativistic constituent-quark model (RCQM) of Refs. [1,2], i.e. with the same linear confinement, but now with a pseu-doscalar boson exchange of a 24-plet and a singlet, thereby including u, d, s, c, and b quark flavors. For the 24-plet GBE only a single mass and a single cut off had to be foreseen with the Goldstone-boson mass equal to the n mass and a n-Q coupling constant derived from the phenomenological n-N coupling constant using the Goldberger-Treiman relation. The two open parameters inherent in the singlet GBE (the no-Q coupling and the corresponding cut off) were adjusted by fitting the baryon spectra. For more details on the parameter values see Refs. [10] or [16]. Since the 2018 Bled Mini-Workshop concentrated on double-charm baryons, we discuss in this contribution only the description of heavy-flavor baryons by the URCQM1. We start with the single-charm spectra in Fig. 1. It is immediately evident that all of the ground states are well reproduced. The same is true with the experimentally established excitations. For the levels in the Ac and Ic spectra, where JP is not definitely known, the URCQM offers nearby levels. The spectra of the double-charm baryons are shown in Fig. 2. Until recently only for the Ecc ground state there were experimental data available from a single experiment, namely the one by the SELEX collaboration [18]. The URCQM produces the Ecc ground state more than 100 MeV higher than these data, precisely at 3642 MeV. Similarly, other theoretical models such as the RCQM by the Bonn group [19] (shown by the cyan lines in Fig. 2) or the lattice-QCD calculation by Liu et al. [20] (given by the magenta boxes in Fig. 2) obtain a Ecc ground-state level by about the same magnitude higher than the SELEX value. However, there has been a recent measurement of the Ecc ground state by LHCb [21] yielding its mass as m = 3621.40±0.72(stat.)±0.27(syst.)±0.14(Ac) MeV. The predictions by the URCQM as well as by the other theoretical calculations are now quite compatible with this value. It will be interesting to obtain phenomeno-logical data also for Ecc resonances. For the sake of future comparisons we give in Tab. 1 the predictions of the UCRQM for the first seven Ecc excitations. We remark that certain J = 2 and J = | resonances are degenerate, the reason being that the UCRQM does not (yet) contain tensor forces in the GBE hyperfine interaction. However, as has been learned in case of the GBE RCQM, the inclusion of 1 The light- and strange-baryon spectra of the URCQM are very similar in most cases identical to the ones of the GBE RCQM of Refs. [1,2]; cf. also Ref. [15]. M [MeV] 310030002900280027002600250024002300- 2200 1+ 2 3 + 2 5 + 2 1 + 2 3 + 2 1 + 2 3 + 2 Ac Sc Qc Fig. 1. Single-charm baryon spectra of definite JP as produced by the URCQM (solid/red levels) in comparison to experimental data with their uncertainties (dotted/green levels resp. boxes) [17]. 2 M [MeV] 4400430042004100400039003800370036003500 1 + 2 3 + 2 1 + 2 3 + 2 Fig. 2. Same as Fig. 1 but for double-charm baryons. The predictions of the URCQM are the solid/red levels. Here they are compared to several other theoretical results and the SELEX experiment for the Scc ground state (lowest/green level) [18]. For further explanations see the text. cc all types of hyperfine forces from GBE does not much change the characteristics of the baryon spectra [22,23]. For completeness of the description of heavy baryons by the URCQM we add the single- and double-b baryons in Figs. 3 and 4. Only for single-b baryons we Universal Constituent-Quark Model for All Baryons 21 Table 1. Scc ground state and its first seven excitations as predicted by the URCQM. State JP URCQM 1 + 2 3 + 2 1- 2 3 -2 1- 2 3 -2 1 + 2 3 + 2 3642 3683 3899 3899 4004 4004 4032 4064 cc cc cc cc cc cc cc cc may compare to experimental data. In all instances we find good agreement with phenomenology. In case of double-b baryons we are left only with comparisons to other effective models, where we now notice bigger discrepancies. By the results shown here together with the ones for the light- and strange baryon sectors reported in Refs. [15] and [10] it is certainly evident that a universal relativistic constituent-quark model may be constructed solely on the basis of Goldstone-boson exchange. While beyond the given confinement all of the masses involved in the hyperfine interaction - for constituent quarks u, d, s, c, and b as well as the exchanged Goldstone bosons n and n - may be taken as predetermined, like the 24-plet coupling constant, there remain only three open fit parameters, the 24-plet as well as the singlet cut offs and the singlet coupling constant. This is certainly remarkable, like the fact that the dynamical ingredients Fig. 3. Single-beauty baryon spectra of definite JP as produced by the URCQM (solid/red levels) in comparison to experimental data with their uncertainties (dotted/green levels resp. boxes) [17]. in the constituent-quark masses (differences between the current and constituent masses) remain practically independent of the flavor [26,27]. Fig. 4. Double-beauty baryon spectra of definite JP as produced by the URCQM (solid/red levels) in comparison to a nonrelativistic one-gluon-exchange constituent-quark model by Roberts and Pervin [24] (green/higher-lying levels) and the RCQM by Ebert et al. [25] (brown/lower-lying levels). Acknowledgement The author is 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 2018 we have enjoyed the 20th edition thereof, and our best wishes are due for many more such Mini-Workshops to happen in the future. Results of the GBE relativistic constituent quark model discussed in this contribution have been obtained in collaboration with Ki-Seok Choi and Joseph P. Day. References 1. L. Y. Glozman, W. Plessas, K. Varga, and R. F. Wagenbrunn, Phys. Rev. D 58, 094030 (1998) 2. L. Y. Glozman, Z. Papp, W. Plessas, K. Varga, and R. F. Wagenbrunn, Phys. Rev. C 57, 3406 (1998). 3. R. F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas, and M. Radici, Phys. Lett. B 511, 33 (2001) 4. K. Berger, R. F. Wagenbrunn, and W. Plessas, Phys. Rev. D 70, 094027 (2004) 5. M. Rohrmoser, K. S. Choi, and W. Plessas, Acta Phys. Polon. Supp. 6, 371 (2013) 6. M. Rohrmoser, K. S. Choi, and W. Plessas, Few-Body Syst. 58, 83 (2017) 7. L. Y. Glozman, M. Radici, R. F. Wagenbrunn, S. Boffi, W. Klink, and W. Plessas, Phys. Lett. B 516,183 (2001) 8. S. Boffi, L. Y. Glozman, W. Klink, W. Plessas, M. Radici, and R. F. Wagenbrunn, Eur. Phys. J. A 14,17 (2002) 9. T. Melde, L. Canton, and W. Plessas, Phys. Rev. Lett. 102,132002 (2009) 10. W. Plessas, Int. J. Mod. Phys. A 30,1530013 (2015) 11. K.-S. Choi and W. Plessas, Few-Body Syst. 54,1055 (2013) 12. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Phys. Rev. D 82, 014007 (2010); ibid. 039901 (2010) 13. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Phys. Rev. C 81, 028201 (2010) 14. K.-S. Choi, W. Plessas, and R. F. Wagenbrunn, Few-Body Syst. 50, 203 (2011) 15. J. P. Day, K.-S. Choi, and W. Plessas, Few-Body Syst. 54, 329 (2013) 16. J. P. Day, PhD Thesis, University of Graz (2013) 17. K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) 18. M. Mattson et al. [SELEX Collaboration], Phys. Rev. Lett. 89,112001 (2002) 19. S. Migura, D. Merten, B. Metsch, and H. R. Petry, Eur. Phys. J. A 28, 41 (2006) 20. L. Liu, H. W. Lin, K. Orginos, and A. Walker-Loud, Phys. Rev. D 81, 094505 (2010) 21. R. Aaij etal. [LHCb Collaboration], Phys. Rev. Lett. 119,112001 (2017) 22. K. Glantschnig, R. Kainhofer, W. Plessas, B. Sengl, and R. F. Wagenbrunn, Few-Body Syst. Suppl. 14, 55 (2003) 23. K. Glantschnig, R. Kainhofer, W. Plessas, B. Sengl, and R. F. Wagenbrunn, Eur. Phys. J. A 23, 507 (2005) 24. W. Roberts and M. Pervin, Int. J. Mod. Phys. A 23, 2817 (2008) 25. D. Ebert, R. N. Faustov, V. O. Galkin, and A. P. Martynenko, Phys. Rev. D 66, 014008 (2002) 26. W. Plessas, in: Proceedings of the Mini-Workshop Quark Masses and Hadron Spectra, Bled, Slovenia, ed. by B. Golli, M. Rosina, and S. Sirca. Bled Workshops in Physics 15, 34 (2014) 27. M. Rosina, in: Proceedings of the Mini-Workshop Quark Masses and Hadron Spectra, Bled, Slovenia, ed. by B. Golli, M. Rosina, and S. Sirca. Bled Workshops in Physics 15, 50 (2014) Bled Workshops in Physics Vol. 19, No. 1 p. 24 Doubly-heavy baryons, tetraquarks and related topics* J.-M. Richarda, A. Valcarceb, J. Vijandec aUniversite de Lyon, Institut de Physique Nucieaire de Lyon, IN2P3-CNRS-UCBL, 4 rue Enrico Fermi, 69622 Villeurbanne, France, b Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca, E-37008 Salamanca, Spain cUnidad Mixta de Investigación en Radiofísica e Instrumentación Nuclear en Medicina (IRIMED), Instituto de Investigation Sanitaria La Fe (IIS-La Fe), Universitat de Valencia (UV) and IFIC (UV-CSIC), Valencia, Spain Abstract. We review the physics of doubly-heavy baryons QQ q and tetraquarks QQ qq. For the latter, the stability is reached for large enough mass ratio M/m, even when spin forces and color mixing are neglected. It is thus customarily claimed that bb q q in its ground state cannot decay into b q + b q. In some model, ccud is shown to be stable if color mixing and spin effects are properly taken into account. It is conjectured that some bc q q' benefits from favorable adjustments of the gluon tubes in the confinement regime. Some recent studies of pentaquarks and hexaquarks are also summarized. 1 Introduction Double-charm physics, and more generally the physics of doubly-heavy hadrons is by now rather old. Shortly after the prediction of charm by the GIM mechanism [1], Lee, Gaillard and Rosner [2] wrote a seminal paper anticipating many interesting properties of charmed hadrons, including double-charm baryons, with an empirical notation which is now obsolete. As indicated in Sec. 3, the first speculations about QQ q q arose in 1981 [3], while the first detailed quark model calculation of the doubly heavy baryons QQ q came in 1988 [4]. Since then, significant progress has been achieved, with in particular the onset of QCD sum rules and lattice QCD, which is discussed elsewhere in these proceedings. Also, the interaction of light quarks is treated more realistically with the implementation of chiral dynamics. In the abundant literature on QQ q and QQ q q, there are also papers with unjustified approximations that do not account for the rich and subtle few-body dynamics inside these hadrons. 2 Doubly-heavy baryons Calculating QQ q in a given quark model is rather straightforward, and there are several interesting studies, e.g., [4-6]. In the wave function of the first levels, * Talk presented by J.-M. Richard one observes a hierarchy of the average separations, r(QQ) C r(Qq), which can be interpreted as a spontaneous or dynamical diquark clustering. But the first excitations occur within the QQ pair and involve a new diquark for each level. A word about diquarks is in order. There are models where diquarks are introduced as basic constituents. They have a number of successes, and also problems, such as deciding which quarks do cluster in q1 q2q3, and explaining some nucleon resonances recently seen in photoproduction, which seemingly require two internal excitations. Much more questionable is the diquark picture just as an approximation, or say a lazy way of handling the three-body problem. If the ground-state of abc is searched by solving first the ab problem with the potential Vab alone, and then the two-body problem [ab]c with Vac(r) + Vbc (r) with r the distance from c to the center of [ab], then the algebraic energy is underestimated. A simple exercise consists of comparing V(r) and the average of V(|r + r'|) when the angles of r' around r are varied. Except in the Coulomb case (Gauss theorem), one finds a non-negligible deviation. In other words, the effective QQ interaction within QQq is influenced by the light quark. Though the Born-Oppenheimer approximation was invented in 1927, it has not yet reached some remote universities. Yet, if any approximation has to be made, this is probably the most interesting. The effective QQ potential in a QQq baryon is the analog of the quark-antiquark potential of charmonium, which itself is also a kind of Born-Oppenheimer potential: the minimal energy of the light degrees of freedom for a given QQQ separation. 3 Tetraquarks with two heavy quarks Estimating the tetraquark energy and structure, even in simple quark models, involves a delicate four-body problem. There is a competition between a collective compact configuration and a breaking into two mesons. Unfortunately, this is not always very well handled in the literature. Some authors consistently mistreated the four-body problem in other fields and in quark models. For some other authors, this is more puzzling, as they have set benchmarks of rigor for quarkonium, but became less and less rigorous as the number of constituents was increased. Corruptio optimorum pessima1 use to say our ancestors. Historically, the first study of QQqq was made at CERN [3], with the observation that the system becomes bound, below the Qq + Qq threshold, if the mass ratio M/m becomes large enough. This was confirmed by Heller et al. [7,8] and Zouzou et al. [9]. The possibility of binding QQqq have been rediscovered in some very recent papers, which are sometimes given credit for this idea. This corresponds to the "11th hour effect", So the last will be first, and the first last (Matthew 20.16). Another sentence of Matthew's Gospel is also cited in such circumstances, in particular by the sociologist R. Merton [10]: For to him who has will more be given; and from him who has not, even what he has will be taken away. 1 The corruption of the best is the worst The binding of QQqq is a chromoelectric effect at start: the tetraquark benefits from the heavy-heavy attraction that is absent form the threshold. It was also realized that chromomagnetic effects could be decisive for ccud, with an attraction in the light sector that is absent in the threshold. A decisive progress was accomplished by Janc and Rosina [11], who showed that ccud is stable in a specific quark model when chromo-electric and magnetic effects are properly combined. Their result was confirmed and improved by Barnea et al. [12]. See, also, [13]. There are very few rigorous results for the four-body problem, besides the ones shared with any N-body problem, such as the virial theorem and the scaling properties in a power-law potential. The physics of tetraquarks, however, stimulated some contributions: the improved stability when charge-conjugation symmetry C is broken, and the improved stability for asymmetric potentials, as explained below. The first point should have been borrowed from atomic physics, but paradoxically, the quark physics helped to understand the transition from the positronium molecule to the hydrogen one [14,15].2. It is well-known that breaking a symmetry lowers the ground-state energy. For instance, going from Ho = p2 +x2 to H0 +Ax lowers the first energy from E0 = 1 to E0 — A2/4, and more generally, breaking parity in H = Heven + Hodd gives E < Eeven. But in a few-body system, the breaking of symmetry often benefits more to the threshold than to the collective configuration and thus spoils the binding. For instance, in atomic physics, going from Ps2 to (M+, m+, M-, m-) makes the system unstable for M/m > 2.2 [17,18]. However, when the symmetry is charge-conjugation, the symmetry breaking benefits entirely to the collective state. Let us, indeed, write the four-body Hamiltonian of the hydrogen molecule as 2 2 2 2 Pi P2 P3 P4 H = 2M + 2M + 2m + 2m + V = Heven + Hodd ( 1 1 A (1) + 4M — 4m (pi2+p22—p32—p42) , Z £ + V where 2 = M-i + m-i. The C-parity breaking term, Hodd, lowers the ground state energy of H with respect to the C-parity even part, Heven, which is simply a rescaled version of the Hamiltonian of the positronium molecule. Since Heven and H have the same threshold, and since the positronium molecule is stable, the hydrogen molecule is even more stable, and stability improves when M/m increases. Clearly, the Coulomb character of V hardly matters in this reasoning, except that if the potential is not Coulombic, Veven does not always support a bound state: in this case, stability occurs starting from a minimal value of M/m. The key assumption is that the potential does not change when the masses are modified, a property named "flavor independence" in QCD. As ever, the Born-Oppenheimer approach is very instructive. If one restricts to color 33, the Born-Oppenheimer QQ potential of QQqq is similar to the one of QQq, up to an overall constant, which can be identified as the mass difference Qqq — Qq from the values at zero separation. See Fig. 1. One thus gets a To be honest, a similar reasoning was already outlined in the physics of excitons [16] microscopic derivation of the Eichten-Quigg identity (here without the spin refinements) [19] QQqq ~ QQq + Qqq - Qq. (2) Of course, with color mixing, the mass of the tetraquark decreases with respect to the above estimate, and this can be decisive in the charm sector. -1-1-1-1-^ x 1 2 3 4 5 Fig. 1. Comparison of the QQ Born-Oppenheimer potentials in QQq (solid line) and QQ q q (dotted line), the latter shifted by the mass difference Qqq — Q q A conservative conclusion, in most studies, is that only bbqq is stable. This is indeed the case if spin corrections and color mixing are neglected. With proper inclusion of both color [QQ][q q] = 33 and 66 states, and spin effects, one gains some binding in the ccud case. This is shown in Fig. 2. Another effect could benefit to bc qq states. A typical quark model potential reads 3 V = —16 LA ^ j 16 T-- Ai > 0, while it is only most plausible if |A2| > |A11 with A1 A2 < 0, as E(A) is nearly parabolic as a function of A. 4 Pentaquarks and hexaquarks Other configurations are regularly revisited, with the hope to predict new stable or metastable multiquarks. In the pentaquark sector, the Qqqqq systems have been revisited. In 1987, it was shown that in the limit where Q is infinitely heavy, and qqqq = uuds, ddus or ssud in the SU(3)F limit, with the assumptions that the strength of the chromo-magnetic term is the same as for ordinary baryons, this state is bound by about 150MeV below the Qq + qqq threshold. This pentaquark was searched for in an experiment at Fermilab [23,24], which turned out inconclusive. The non-strange variant was studied at HERA [25,26]. More precisely, if A = j CTtCTj) is the expectation value of the chro- momagnetic operator for N or A, then Q qqqq gets 2 A in the most favorable case. In further studies, it was noticed that as in the case of the famous H = uuddss, the multiquark wave function is more dilute than the baryon wave function. This reduces the effectiveness of the chromomagnetic interaction. This is confirmed in our recent study. Two contributions deal with the hidden-charm states, say QQqqq, which have been much studied after the discovery of the so-called LHCb pentaquarks [27]. First, it is found that within a standard quark model of the type (3), some states are likely below the threshold [28]. This means that new pentaquarks perhaps await discovery, with different quantum numbers. Another study deals with the states in the continuum. In the early days of the quark model applied to the multiquark sector bound-state techniques were innocently applied to resonances, with the belief that if a state if found, say, 100 MeV above the threshold using a crude one-Gaussian variational wave function, a resonance is predicted at about this energy! The method of real scaling was applied recently to ccuud [29], using a standard quark model. It is found that one can separate clearly states that just mimic the continuum from genuine resonances. This is very encouraging, though the candidates for (3/2)- or (5/2)- are significantly higher that the LHCb pentaquarks. In the hexaquark sector, there is a continuous effort from many authors. Our contribution deals with QQqqqq, that looks at first very promising, as it combines the chromoelectric attraction of the QQ pair, which acts in the threshold QQq + qqq, but not in Qqq + Qqq, and the chromomagnetic attraction which is more favorable in the latter than in the former threshold. Moreover, for qqqq = uuds, ddsu or ssud, the same coherence as in the Q qqqq pentaquark could help. However, our study shows that the various effects hardly act together, as each of them requires a specific color-spin configuration. 5 Outlook The physics of multiquark is of primordial importance for hadron spectroscopy. The constituent models, however simple, are a good guidance before considering more ambitious theories. They require some care, but benefit of the know-how accumulated in other branches of few-body physics. Some further developments are required for describing states in the continuum. The method of real scaling looks rather promising, but might be challenged by other schemes. The coupling of channels also reveals interesting features and offers a somewhat complementary point of view [30,31]. The transition from short-range dynamics in terms of quarks, to a long-range hadron-hadron dynamics is probably the key to describe most of the states. Acknowledgments JMR would like to thank M. Rosina and his colleagues for the friendly and stimulating atmosphere of the Bled meeting, and also E. Hiyama, M. Oka and A. Hosaka for a fruitlful collaboration about states in the continuum. References 1. S. L. Glashow, J. Iliopoulos, and L. Maiani. Phys. Rev., D2:1285-1292,1970. 2. M. K. Gaillard, B. W. Lee, and J. L. Rosner. Rev. Mod. Phys., 47:277-310,1975. 3. J. P. Ader, J. M. Richard, and P. Taxil. Phys. Rev., D25:2370,1982. 4. S. Fleck and J. M. Richard. Prog. Theor. Phys., 82:760-774,1989. 5. D. U. Matrasulov, M. M. Musakhanov, and T. Morii. Phys. Rev., C61:045204, 2000. 6. J. Vijande, H. Garcilazo, A. Valcarce, and F. Fernandez. Phys. Rev., D70:054022, 2004. 7. L. Heller and J. A. Tjon. Phys. Rev., D35:969,1987. 8. J. Carlson, L. Heller, and J. A. Tjon. Phys. Rev., D37:744,1988. 9. S. Zouzou, B. Silvestre-Brac, C. Gignoux, and J. M. Richard. Z. Phys., C30:457,1986. 10. R. K. Merton. Science, 159:56-63, January 1968. 11. D. Janc and M. Rosina. Few Body Syst., 35:175-196, 2004. 12. N. Barnea, J. Vijande, and A. Valcarce. Phys. Rev., D73:054004, 2006. 13. A. Czarnecki, B. Leng, and M. B. Voloshin. Phys. Lett., B778:233-238, 2018. 14. J. M. Richard. In Quark cluster dynamics. Proceedings, 99th WE Heraeus Seminar, Bad Honnef, Germany, June 29-July 1,1992, pages 84-91,1992. 15. J.-M. Richard, J. Fröhlich, G.-M. Graf, and M. Seifert. Physical Review Letters, 71:13321334, August 1993. 16. J. Adamowski, S. Bednarek, and M. Suffczynski. Philosophical Magazine, 26:143-151, July 1972. 17. D. Bressanini, M. Mella, and G. Morosi. theoretical and quantum monte carlo study of biexciton molecules. Phys. Rev. A, 57(6):4956-4959, Jun 1998. 18. K. Varga, J. Usukura, and Y. Suzuki. In B. Desplanques, K. Protasov, B. Silvestre-Brac, and J. Carbonell, editors, Few-Body Problems in Physics '98, page 11,1999. 19. E. J. Eichten and Ch. Quigg. Phys. Rev. Lett, 119(20):202002, 2017. 20. J. Vijande, A. Valcarce, and J-M. Richard. Phys.Rev., D85:014019, 2012. 21. J. Vijande, A. Valcarce, and J.-M. Richard. Phys. Rev., D87(3):034040, 2013. 22. E. A. Hylleraas and A. Ore. Phys. Rev., 71(8):493-496, Apr 1947. 23. E. M. Aitala et al. Phys. Rev. Lett., 81:44-48,1998. 24. E. M. Aitala et al. Phys. Lett., B448:303-310,1999. 25. A. Aktas et al. Phys. Lett., B588:17, 2004. 26. S. Chekanov et al. Eur. Phys. J., C38:29-41, 2004. 27. R. Aaij et al. Phys. Rev. Lett., 115:072001, 2015. 28. J. M. Richard, A. Valcarce, and J. Vijande. Phys. Lett, B774:710-714, 2017. 29. E. Hiyama, A. Hosaka, M. Oka, and J.-M. Richard. Phys. Rev., C98(4):045208, 2018. 30. J. Vijande, A. Valcarce, J.-M. Richard, and N. Barnea. Few-Body Systems, 45:99-103, May 2009. 31. H. Garcilazo and A. Valcarce. Eur. Phys. J., C78(3):259, 2018. Bled Workshops in Physics Vol. 19, No. 1 p. 32 Production of Pairs of Heavy Quarks by Double Gluon Fusion D. Treleani Physics Department, University of Trieste and Trieste Section of INFN 1 Double Parton Interactions The rapid growth of the parton flux at small x gives rise to a dramatic increase of cross sections with large momentum transfer in pp collisions at high energies. In the case of production of mini-jets at the LHC, the inclusive cross section may in fact exceed the value of the total inelastic cross section, for not unrealistically small values of the transverse momenta. One faces therefore a unitarity problem with the large momentum transfer cross sections at high energies, which is solved by introducing Multiple Parton Interactions (MPI) in the process. MPI take into account the possibility of having two or more elementary partonic interactions in a given inelastic hadronic collision and unitarity is restored by MPI because the inclusive cross section is proportional to the multiplicity of interactions. In this way, the inclusive cross section is no more bounded by the value of the total inelastic cross section, when the average multiplicity of interactions is large. The simplest case of MPI is Double Parton Scattering (DPS). When looking for MPI, one should keep into account that, hard interactions are localised in a space region much smaller as compared to the hadron size and, once the final state is given, the main contribution from MPI is due to the processes which maximise the incoming parton flux. In DPS the hard component of the interaction is thus disconnected and the non-perturbative components are factorised into functions which depend on two fractional momenta and on the relative transverse distance b between the two interaction points. The non-perturbative input to the DPS cross section, namely the double parton distribution functions, depend therefore explicitly on the relative transverse distance b. By neglecting spin and color, the inclusive double parton-scattering cross-section, for two parton processes A and B in a pp collision, is given by [1]: ct(A,B) 1 + 6 A,B Y_ Ti,j (xi,X2; b)^Ak(xi,xi Bi(x2,x2)rk,i(xi,x2; b) x dxi dxj dx2 dx2 d2b (1) where the Ts represent the double parton distributions and the elementary partonic cross sections. Notice that the dependence of B) on the total transverse energy, of the final state partons with a large pt, is very well characterised and very strong: it is in fact equal to the square of the dependence on the total transverse energy of a single hard scattering cross section. The characteristic dependence of the DPS cross section on the total transverse energy of final state partons with large pt represents therefore a rather non trivial experimental test of the interaction dynamics. One may include all unknowns in the process in a quantity with dimensions of a cross section, the effective cross section, and the inclusive DPS cross section can thus be expressed by the simplest pocket formula, widely used in the experimental analysis of DPS processes: D 1 OA 0"B 0, while the quark mass in this limit behaves as 9CT(T) gf q X(r) X(r) , which means that the quarks are bound. A typical self-consistent solution for the fields is shown in Fig. 1 a). 2 1.5 1 0.5 0 1.5 - ^u(r) 1/x(r) 1 - / 0.5 a(r) 0 -0.5 _ n(r) x(r) v(t) -1 -1.5 0 0.5 r [fm] a) 1.5 (r) £1 U,(r) mff = 0.7 GeV mff = 0.6 GeV mff = 0.5 GeV mff = 0.4 GeV 0.5 1 1.5 r [fm] b) Fig. 1. a) Self-consistently determined quark and boson (in units of fn) fields in the CDM. b) Effective potential for the ct meson and the lowest eigenvalue £ 1 of the corresponding Klein-Gordon equation (in units of GeV) for different choices of the ct mass. 0 2 We next expanded the field operators of the bosons around their expectation values in the ground state |N); the a operator can be written as: fr(r) = V Vn(r)-L [an + an] + a(r), oJN) = 0. The stability conditions implies a Klein-Gordon equation for the a-meson modes: (-V2 + m2ff + UCT(r)) ^n(r) = £n?n(r) , Uff (r) = . da(r)2 Here V stands for the potential originating from (1) and the potential parts of the a-model. The potential UCT (see Fig. 1b)) is attractive and supports a bound state which can be interpreted as a molecular state of the nucleon and (one quantum of) the a. The corresponding potential for the x field turns out to be repulsive, which means that the model does not predict glueball states. In [10] this excitation of the a field was confronted with the excitation of the quark core in which one quark wass promoted to the 2s orbit. In the self-consistent solution the 2s — Is energy splitting turned out to be smaller than the corresponding vibrational energy ei, and the conclusion of our work was that the Roper consisted of the dominant quark excitation and a ~ 10 % admixture of the molecular state. However, in that work we used - in accordance with then accepted values - a relatively large a mass between 0.7 GeV and 1.2 GeV. With the present value ~ 0.5 GeV, the lowest eigenmode e1 decreases (see Fig. 1b)), while, assuming a somewhat smaller nucleon size, the 2s — 1s splitting increases, such that the molecular state may eventually become the dominant component of the Roper resonance. In our recent paper [1] we study the formation of the resonance in this partial wave in a coupled-channel approach including the nN, nA and aN channels. The Cloudy Bag Model is used to fix the quark-pion vertices while the s-wave abaryon vertex is introduced phenomenologically with the coupling strength gCT as a free parameter and two choices for the mass and the width of the a meson, mCT = rCT = 0.6 GeV and mCT = TCT = 0.5 GeV. 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: a? ky) = K ay (ka,kT) + ^ p dk Kap (ka, k)XftY (k, ky) w(k) + Ep(k) — W Approximating the kernel K by a separable form, the integral equation reduces to a system of linear equations which can be solved exactly. For sufficiently strong coupling gCT the kernel K may become singular and a (quasi) bound state arises. 0.4 0.2 1.1 1.2 1.3 1.4 1.5 1.6 1.7 W [GeV] Fig. 2. The lowest eigenvalue wmin for four different values of the aN coupling. 9a ReWp —2ImWp [GeV] [GeV] PDG 1.370 0.175 1.80 1.397 0.157 1.95 1.383 0.112 2.00 1.358 0.111 2.05 1.331 0.044 1.438 0.147 Table 1. Poles in the complex W-plane for four typical values of gCT. The PDG values are from [11]. 0 In order to study this process we follow the evolution of the lowest eigenvalue of the matrix pertinent to the system of linear equations, wmin, as a function of W for different values of gCT (see Fig. 2). Along with this evolution we observe the evolution of the resonance S-matrix pole in the complex W-plane using the Laurent-Pietarinen expansion [12-15] (see Table 1). We see that the lowest eigenvalue indeed touches the zero line for gCT = 2.0, the pole, however, emerges already for considerably weaker couplings and starts approaching the real axis. Beyond the critical value, wmin crosses zero twice, producing two poles in the complex energy plane. It is interesting to note that for the values below the critical value, the real part of the pole position almost coincides with W at which wmin reaches its minimum. This value of W is of the order of 100 MeV below the nominal ctN threshold. The result agrees well with the molecular picture of the Roper resonance discussed in the first part of this contribution. Let us note that because the ctN channel is coupled to other channels, the molecular state has a finite width (i.e. finite ImWp) even for gs greater than the critical value. In the present approach we have also studied the influence of including a genuine three quark state with one quark excited to the 2s orbit. Using gCT « 1.5, the results for the position as well as the modulus and the phase come close to the PDG value [11], and are rather insensitive to the mass of the genuine three-quark state. This leads us to the conclusion that the mass of the S-matrix pole is determined by the energy of the molecular state while its detailed properties may still considerably depend on the three-quark excited state. The simple model discussed in the first paper provides a simplified picture which enables a deeper insight into the mechanism of the resonance formation, hindered by the complex formalism of the coupled-channel approach. 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. P. Alberto, L. Amoreira, M. Fiolhais, B. Golli, and S. Sirca, Eur. Phys. J. A 26, 99 (2005). 5. B. Golli and S. Sirca, Eur. Phys. J. A 38, 271 (2008). 6. B. Golli, S. Sirca, and M. Fiolhais, Eur. Phys. J. A 42,185 (2009). 7. B. Golli, S. Sirca, Eur. Phys. J. A 47, 61 (2011). 8. B. Golli, S. Sirca, Eur. Phys. J. A 49,111 (2013). 9. B. Golli, S. Sirca, Eur. Phys. J. A 52, 279 (2016). 10. P. Alberto, M. Fiolhais, B. Golli, and J. Marques, Phys. Lett. B 523, 273 (2001). 11. M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98 , 030001 (2018). 12. A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, L. Tiator, and R. L. Workman, Phys. Rev. C 88, 035206 (2013). 13. A. Svarc, M. Hadzimehmedovic, R. Omerovic, H. Osmanovic, and J. Stahov, Phys. Rev. C 89, 045205 (2014). 14. A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, and R. L. Workman, Phys. Rev. C 91, 015205 (2015). 15. A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, L. Tiator, and R. L. Workman, Phys. Rev. C 89, 065208 (2014). Bled Workshops in Physics Vol. 19, No. 1 p. 41 Double charm baryons and dimesons 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. Several constituent quark models more or less agree in the descripton of baryons and mesons. They may, however, largely disagree in their predictions for dimesons (tetraquarks). The cleanest systems may be ccud = DD* and bbud = (bb)ud. In view of Belle II experiments (at KEK, Japan) in near future, it is of interest to study the DD* dimeson, in order to gain some understanding of the production and detection mechanism and to give some guidance to experimentalists. 1 Introduction There is a strong motivation to verify whether we are capable to extrapolate our experience in QCD from baryons and mesons to many-quark systems. At the level of model-making, it is of interest to look at dimesons (tetraquarks), pen-taquarks and dibaryons (hexaquarks). 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 = Vcc = Vbu = Vbb = Vbb. The obvious system worth studying is the DD* system which is expected to be either a weakly bound "molecule" or a low-lying resonance. It is relatively long-lived since it decays only electromagnetically (D*—>Dy) or strongly with extremely small phase space (D*—>Dn). Note that the DD system is a bad candidate since D+D repel each other and no bound state forms. After the discovery of the E++ = ccu baryon at LHCb, there is a revived interest for the search of the double charm dimesons. The production mechanism might be similar, but the detection of dimesons is more difficult. For the double charm baryon, they analysed the resonant decay E++ —» A+K-n + n+ where the A baryon was reconstructed in the decay mode A+ —» pK-n+. There is no such clear production and detection process available for the DD* intermediate state and it is a great challenge to find a mesurable signature for this dimeson. 2 The binding energy of the E++ baryon There is a controversy regarding the mass of the double charm baryon. The better documented value of E++ from LHCb is 3621 MeV while the SELEX value 3519 'cc MeV of —> A+K-n+ is met with some scepticism. It would be good to find out whether these are two different states, or SELEX is wrong. We made a phenomenological estimate using a diquark-quark model and the analogy with mesons (fig.1). Regarding colour quantum number, the diquark in an antisymmetric colour state behaves just as an antiquark. We took a nonrela-tivistic potential model with a one-gluon-exchange + confining potential with the "Grenoble parameters AL1" [1] which reproduce rather well most baryons and mesons, in particular also J/^, the analogon of cc. We get for the mass of the cc diquark 3500 MeV. Fig. 1. The comparison of the S++ baryon with the ID0 and B+ mesons Using m(c)=1870 MeV, m(D0)=1865 MeV, m(b)) = 5259 MeV and m(B+)=5279 MeV we get m(E+c+) = m(D0) - m(c) + m(cc) = 3495 MeV or m(E+c+) = m(B+) - m(b) + m(cc) = 3520 MeV. At face value, the latter estimate is very close to the SELEX value. However, the finite size of the diquark and the extra Coulomb repulsion will raise the mass, possibly close to the LHCb value. Let me quote also other results. Plessas - the Graz group [2] - obtained with the "Universal constituent quark model for all baryons" (relativistic kinetic energy and a one-Goldston-boson- exchange interaction for the 24-plet + singlet with 5 flavours) the E+c+ mass 3642 MeV. cc The Lattice QCD result [3] is also around 3600 MeV. 3 The binding energy of the D+D* dimeson In the restricted 4-body space assuming "cc" in a bound diquark state and the u and d quarks in a general wavefunction, the energy is above the D+D* threshold. In the restricted "molecular" 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. Only combining both spaces brings the energy below the threshold. In the nonrelativistic calculation of Janc and Rosina [4] the one-gluon exchange potential (including the chromomagnetic term) + the linear confining potential was used. The model parameters (Grenoble AL1) [1] fitted all relevant mesons and baryons. A rich 4-body space was used (an s-state Gaussian expansion at optimized distances, with 3 types of Jacobi coordinates in order to mimic also the p-states. The binding energy (DD*) - (D + D*) = - 2.7 MeV was obtained. This is encouraging, but we have to explore in future, what happens with other interactions and whether the pion cloud between the u and d antiquarks can increase binding, in analogy with the deuteron. 4 The formation and decay of the DD* dimeson There are two possible mechanism for the formation of the dimeson: 1. In the first step the cc-diquark is formed and later automatically dressed by u + cl (or u or d or s in the case of Ecc and Hcc). We have estimated the relative probability of forming ccu or ccd or ccs or the "atomic" configuration ccud by analogy with the dressing of the b quark into B+, B0, B° and the Ab baryon determined experimentally in ref. [5]. Initially the relative probability of forming (cc)ud is about 9% which is about 1/4 probability with respect to E+c+ (table 1). Quite a lot! However, this percentage is further reduced by the evolution of the "atomic" configuration (cc)ud into the "molecular" configuration of DD*. Mind that the atomic configuration is almost 100 MeV above the D + D* threshold and would decay mostly into two free mesons. The question remains, whether it will decay copiously enough through the DD* bound state or resonance which we are searching for. Table 1. The estimated probability of formation of the tetraquark configuration cc lid b^ B- =bu 0.375±0.015 cc —> S++ = ccu 37% B0 = bd 0.375±0.015 "CC = ccd 37% Bs=bs 0.160±0.025 n+c = ccs 16% Ab = bud 0.090±0.028 T+C = cc ud 9% 2. In the first step two separate mesons D and D* are formed and then they merge into the DD* dimeson. This process might profit from resonance formation, but due to the dense environement there is a danger that the D + D* system would dissociate before forming the dimeson. The question remains how to distinguish these two mechanisms by analysing the decay products. The DD* dimeson is stable against a two-body decay into D+D due to its quantum numbers I=0, J=1. It can decay, however, strongly in D+D+n, or electro-magnetically in D+D+y, via the decay of D*. The strong decay is very slow (comparable to the electromagnetic decay) due to the extremely small phase space for the pion. Therefore, the DD* dimeson is "almost stable" and very suitable for detection. One possibility of detection related to the small phase space of the pionic decay has been proposed by Janc [4,6]. The ratio between the pionic and gamma decay will strongly depend on the binding or resonance energy of the dimeson. For binding energy more than about 5 MeV there will be only y decay. But there will be a strong background due to the decay of free B* and some kinematical analysis is needed to distinguish it. 5 Conclusion More work is needed to predict theoretically the mechanism of formation of the DD* dimeson and to suggest to experimentalists a reliable signature or tagging. References 1. B. Silvestre-Brac, Few-Body Systems 20 (1996) 11. 2. W.Plessas, these Proceedings. 3. Padmanath Madanagopalan et al., Phys.Rev.D 91 (2015) 094502. 4. D. Janc and M. Rosina, Few-Body Systems 35 (2004) 175-196; also available at arXiv:hep-ph/0405208v2. 5. T. Affolder et al. (CDF Collaboration), Phys. Rev. Lett. 84 (2000) 1663. 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. Bled Workshops in Physics Vol. 19, No. 1 p. 45 Pion electroproduction in the energy region of the Roper resonance S. Sircaa'b a Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19,1000 Ljubljana, Slovenia b Jozef Stefan Institute, Jamova 39,1000 Ljubljana, Slovenia The most detailed and model-independent experimental studies of the structure of the Roper resonance utilize coincident electron scattering, in particular in the neutral-pion electroproduction channel. The most recent such study, exploiting polarization degrees of freedom to enhance the sensitivity to the pertinent electro-production multipoles, has been performed at the three spectrometer facility of the A1 Collaboration at the Mainz Microtron (MAMI) [1]. The p(e, e'p)n0 process has been investigated at W « (1440 ± 40) MeV, Q2 « (0.1 ± 0.02)(GeV/c)2 and e; « (90 ± 15)°. Two helicity-dependent recoil polarization components, P^ and P^, have been extracted, as well as the helicity-independent component Py. and compared to the values calculated by MAID [2], DMT [3] and SAID [4]. No model reproduces all features of the data simultaneously. The scalar helicity amplitude ST/2 — sensitive to potentially large pion-cloud effects at such small Q2 — has also been determined. Fixing the transverse helicity amplitude AT/2 to its MAID value and taking SM/2ID as the nominal best model value, we have been able to express ST/2 from our fit as the fraction of SM/2ID, resulting in St/2 = (0.80+0:25) SM/2ID = (14.1+2:5) ■ 10-3GeV-1/2 . References 1. S. Stajner et al., Phys. Rev. Lett. 119 (2017) 022001. 2. D. Drechsel, S. S. Kamalov, and L. Tiator, Eur. Phys. J. A 34 (2007) 69. 3. G. Y. Chen, S. S. Kamalov, S. N. Yang, D. Drechsel, and L. Tiator, Phys. Rev. C 76 (2007) 035206. 4. R. A. Arndt, W. J. Briscoe, M. W. Paris, and I. I. S. R. L. Workman, Chin. Phys. C 33 (2009) 1063. Bled Workshops in Physics Vol. 19, No. 1 p. 46 Discussion sessions Workshop participants At the Mini-workshop Bled 2018, there were also two discussion sessions with informal presentations and discussions. Bogdan Povh (Heidelberg) described new ideas how to explain the well-known deficit in the nucleon spin polarization. It can be better understood if the x-dependence of the polarized structure functions is analysed and not only their integral. He found that the measured structure function agrees with the prediction of the static quark model for Bjorken variable x > 0.2 and drops rapidly for x < 0.2. The interpretation is that for x > 0.2 electrons get scattered quasi-elastically on the undamaged constituent quarks and for x < 0.2 on the fragmented constituent quarks which do not preserve the polarization. In Fig. 1 the x-dependence of the static constituent quark model is represented by the unpo-larized structure function Fp (x) (full line). Fig. 1. Comparison of the prediction of the statical model (full line) and the data for the polarized structure function. Full derivation was presented later at the workshop on Diffraction and Low-x in Reggio Calabria (Aug. 26 - Sept. 1, 2018) [1]. The second discussion session was devoted to the news from Lattice QCD. Sasa Prelovsek (Ljubljana) reported her work on QCD at high temepartures and 0. 07 10"2 X 10° its symmetries from a lattice study [2]. The observed degeneracies in the spectrum are similar to Glozman's depleted spectrum at T=0. The additional chiral-spin symmetry SU(2)Cs appears, as well as a SU(4) symmetry in the limit of high T, even if these symmetries are not present in the Lagrangian. The SU(2)CS symmetry manifests itself in the degeneracy of the vector and tensor-vector spatial correlators as the temperature is increased to about T = 380 MeV (Fig. 2 b)). At this temperature the ratio of these correlators, that are not related by the chiral transformation, approaches one. £ 101 o~ I 1 I 1 I 1 I 1 I 1 I 1 I 1 I U(Da I- ^ 220MeV ^ 260MeV b-h 320MeV g-o 380MeV — free ......... 0 2 4 6 8 10 12 14 16 n 0 2 4 6 8 10 12 14 16 n a) b) Fig. 2. Ratios of normalized correlators, that are related by U(1)A and SU(2)CS symmetry. References 1. B.Povh and M.Rosina, arXiv:1810.11786v1. 2. C. Rohrhofer, Y. Aoki, G. Cossu, L. Ya. Glozman, S. Hashimoto, S. Prelovsek, arXiv:1809.00244 v2. Povzetki v slovenščini Mezonski spektri: eksperimentalni podatki in njihovo tolmačenje E. van Beverena, G. Ruppb a Centro de Física da Universidade de Coimbra, Departamento de Física, Universidade de Coimbra, P-3004-516 Coimbra, Portugal b Centro de Física e Engenharia de Materiais Avancados, Instituto Superior Tecnico, Universidade de Lisboa, P-1049-001 Lisboa, Portugal Pomembno je pravilno tolmačenje eksperimentalnih podatkov. Predvsem poudarjamo, da bi morali spektre sistemov kvark-antikvark proucevati iz konfiguracijz dobrimi kvantnimi stevili, pri tem paje najprimernejši sistem carmonij. Predlagamo moZna bodoca odkritja na podlagi obstojecih slabih podatkov o carmoniju in botomoniju. Pregledamo tudi nasa zapaZanja glede bozonov E(38 MeV) in Z(57.5 GeV). Spektroskopija teZkih barionov v kromodinamiki na mreZi M. Padmanath Institut für Theoretische Physik, Universitat Regensburg, D-93040 Regensburg, Germany V tem porocilu obravnavam najnovejse in najnatancnejse ocene mas barionov v osnovnem stanju z uporabo kromodinamike na mrezi. Glede na dobre izglede za podrocje tezkih barionov poudarjam zlasti ocene zanje. Obravnavam tudi prvo in edino dolocitev visokih vzbujenih stanjbariona Hc na mrezi v povezavi z nedavnim odkritjem na LHCb. Univerzalni model iz konstituentnih kvarkov za vse barione W. Plessas Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria Obravnavamo uspesno delovanje relativisticnega modela iz konstituentnih kvarkov, ki smo ga izdelali kot splosno orodje za opis vseh znanih barionov. Naj-prejponovimo nekajodlocilnih znacilnosti lahkih barionov, potem pa se osre-dotocimo na spektroskopijo barionov, ki vsebujejo kvarke c in b. Dvojno težki barioni in tetrakvarki ter sorodni sistemi J.-M. Richarda , A. Valcarceb, J. Vijandec a Universite de Lyon, Institut de Physique Nucieaire de Lyon, IN2P3-CNRS-UCBL, 4 rue Enrico Fermi, 69622 Villeurbanne, France b Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca, E-37008 Salamanca, Spain c Unidad Mixta de Investigación en Radiofísica e Instrumentación Nuclear en Medicina (IRIMED), Instituto de Investigacion Sanitaria La Fe (IIS-La Fe), Universitat de Valencia (UV) and IFIC (UV-CSIC), Valencia, Spain Podam pregled fizike dvojno teZkih barionov QQq in tetrakvarkov QQqq. Te zadnji postanejo stabilni pri dovolj velikem razmerju mas M/m , tudi ce zanemarimo spinske sile in mesanje barv. Obicajno zatrjujejo, da bbqq v osnovnem stanju ne more razpasti v bq + bq. V nekaterih modelih pa so pokazali, da je tudi ccqq stabilen, ce pravilno upostevamo mesanje barv in spinske efekte. Domnevamo, da nekatera stanja bcqq' lahko izkoristijo ugodne prilagoditve cevi gluonov v podrocju konfinacije. Omenim tudi nekatere nedavne raziskave pentakvarkov in heksakvarkov. Proizvodnja parov težkih kvarkov ž dvojnim gluonskim zlivanjem D. Treleani Physics Department, University of Trieste and Trieste Section of INFN Hiter porast toka partonov z majhnim delezzem gibalne kolicine x povzroci dramaticno povecanje preseka pri trkih visokoenergijskih protonov na protonih. Inkluzivni presek za mini-pljuske lahko presezze celotni neelasticni presek. Problem unitarnosti resi vpeljava vecpartonske (vsaj dvopartonske) interakcije. Vpeljemo kot parameter efektivni presek, ki vkljucuje vse neznane kolicine pri procesu, in uspesno razlozzimo dvojno produkcijo mezonov J/^. Pri majhnih invariantnih masah prevledujejo enojni trki partonov, pri velikih invariantnih masah pa dvojni. Roperjeva resonanca kot molekulsko stanje bariona in mezona B. Golli Pedagoska fakulteta, Univerza v Ljubljani, Ljubljana, Slovenija in Institut J. Stefan, Ljubljana, Slovenija Mehanizem, ki smo ga pred kratkim predlagali za opis nastanka Roperjeve resonance, pri katerem igrata enako pomembni vlogi dinamicno generirano stanje in vzbujeno stanje treh kvarkov, konfrontiramo z modelom, predlaganim pred skoraj dvajsetimi leti, v katerem Roperjevo resonanco obravnavamo kot molekulo, sestavljeno iz nukleona in mezona sigma Dvojno čarobni barioni in dimezoni 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 Mnogi modeli iz konstituentnih kvarkov se bolj ali manj ujemajo pri opisu mezonov in barionov. Lahko se pa močno razlikujejo pri napovedih za dimezone (tetrakvarke). Naj-čistejsa sistema utegneta biti ccud = DD* in bbud = (bb)ud. Glede na bodoče meritve z detektorjem Belle II na Japonskem se izplača proučevati dimezone DD*, da bi bolje razumeli mehanizem proizvodnje in prepoznavanja in bi s tem dali nekaj opore eksperimentalčem. Pionska elektroprodukcija v energijskem področju Roperjeve resonance Simon Sirča Fakulteta za matematiko in fiziko, Univerza v Ljubljani, Jadranska 19, P.O.Box 2964,1001 Ljubljana, Slovenija in Institut Jozef Stefan, 1000 Ljubljana, Slovenija Roperjeva resonanča in njena elektromagnetna struktura sodita med pomembne neresene uganke sodobne hadronske fizike. Lastnosti tega najnizjega vzbujenega stanja nukleona z istimi kvantnimi stevili so tezko dostopne, saj je resonanča skrita pod velikim ozadjem sosednjih resonanč. V prispevku smo poročali o meritvi polarizačijskih komponent odrinjenega protona iz pročesa p(e, e'p)n0, in sičer od vijačnosti odvisnih PxX, PZ ter od vijačnosti neodvisne Py. Rezultate smo primerjali z modelskimi izračuni MAID, DMT in SAID ter ugotovili neujemanje zlasti pri slednjih dveh. Ob določenih modelskih privzetkih smo določili tudi skalarno vijačnostno amplitudo S-|/2. Diskusije Udelezenči delavniče Imeli smo tudi dve srečanji z neformalnimi predstavitvami in diskusijami. Bogdan Povh (Heidelberg je predstavil novo zamisel, kako razloziti znani primanjkljajpri po-larizačiji nukleonovega spina. Ce pogledamo odvisnost polarizirane strukturne funkčije v odvisnosti od deleča gibalne količine x (in ne, kot običajno, le njenega integrala), vidimo, da nastopi primanjkljajpri majhnih x. To pojasnimo, da se elektroni pri x > 0,2 sipljejo na čelem kvarku, pri x < 0,2 pa na "razbitinah" kvarka. Sasa Prelovsek (Ljubljana) pa je poročala o svojem delu na kromodinamiki na mrezi pri visokih temperaturah. Pojavi se degeneračija v spektru, ki kaze na dodatni simetriji SU(2)Cs in SU(4), ki nista prisotni v Lagrangevi funkčiji. Blejske Delavnice Iz Fizike, Letnik 19, št. 1, ISSN 1580-4992 Bled Workshops in Physics, Vol. 19, No. 1 Zbornik delavnice 'Dvojno čarobni barioni in dimezoni', Bled, 17. - 23. junij2018 Proceedings of the Mini-Workshop 'Double-charm baryons and dimesons', Bled, June 17-23, 2018 Uredili in oblikovali Bojan Golli, Mitja Rosina, Simon Sirca Clanki so recenzirani. Recenzijo je opravil uredniski odbor. Izid publikacije je financno podprla Javna agencija za raziskovalno dejavnost RS iz sredstev drzavnega proracuna iz naslova razpisa za sofinanciranje domacih znanstvenih periodicnih publikacij. Tehnicni urednik Matjaz Zaversnik Zalozilo: DMFA - zaloznistvo, Jadranska 19,1000 Ljubljana, Slovenija Natisnila tiskarna Itagraf v nakladi 65 izvodov Publikacija DMFA stevilka 2076 Brezplacni izvod za udelezence delavnice