Bled Workshops in Physics Vol. 16, No. 1 p. 27
A
Proceedings of the Mini-Workshop
Exploring Hadron Resonances
Bled, Slovenia, July 5 - 11, 2015

Resonances in the Constituent-Quark Model*
R. Kleinhappel and W. Plessas
Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria
Abstract. We give a short account of the present description of baryon resonances within the relativistic constituent-quark model, where resonances are usually treated as excited bound states, and point to ways for a more realistic theory producing the resonances as complex poles in the momentum/energy planes, i.e. with real mass values and finite widths.
Nowadays the relativistic constituent-quark model, especially the one relying on a dynamics of linear confinement and a hyperfine interaction of Goldstone-boson exchange [1,2], can provide a reasonable description of the baryon spectra (see, e.g., the recent review in ref. [3]. It is even possible to reproduce - with only a few exceptions - the real mass values of all known baryon ground and resonant states with flavors u, d, s, c, and b in a universal framework in close agreement with phenomenology or data from lattice chromodynamics (QCD) [4-7]. Herein baryons are considered as relativistic bound states of three confined constituent quarks Q interacting mutually. The Q's are supposed to be quasi-particles with dynamical masses generated by the spontaneous breaking of chiral symmetry (SBxS) of low-energy QCD [8,9]. The most important ingredients in the three-Q invariant mass operator turn out to be SBxS and relativistic invariance [10].
Solving the three-Q mass-operator eigenvalue problem provides also access to the baryon eigenfunctions (see, e.g., their rest-frame spatial representations in ref. [12]). They can be subject to tests in various baryon reactions. While their structures appear to be quite reasonable for the baryon ground states, the resonance wave functions are obviously affected by shortcomings.
In particular, the electromagnetic form factors of the nucleons as well as their electric radii and magnetic moments are reproduced in good agreement with phenomenology [13], even with regard to their flavor contents [14]. Similarly, the electromagnetic form factors, electric radii, and magnetic moments of the A and hyperon ground states are found well compatible with available data from experiment and lattice QCD [15,16]. The same is true with regard to the axial form factors and axial charges [16-18]. Likewise, the gravitational form factor A(Q2) of the nucleons is reasonably reproduced [3]. In addition, for the strong form factors of the nNN and nNA a microscopic explanation is provided that conforms with the ones usually adopted in nN and nA dynamical models [19].
* Talk delivered by by W. Plessas
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R. Kleinhappel and W. Plessas
Disturbing shortcomings of the three-Q constituent-quark model appear with regard to direct predictions for hadronic decays of the n, n, and K meson modes. First fully relativistic results in general show an undershooting of the experimental decay widths [12,20-22]. This hints to missing ingredients in the adopted approach. The problems may either be connected with an improper treatment of the meson-decay vertex or missing degrees of freedom from the decay channels.
In order to remedy the situation we have recently adhered to a coupledchannels formalism, taking into account mesonic decays channels explicitly. First attempts along a toy model for mesons yielded promising results [23]. At least it could be shown, how finite resonance widths well develop in such an approach.
Further studies concerned explicit pionic effects both on the ground state and resonance masses (including the resonance widths), exemplified for the nucleon and the A. Details of the formalism and first results were presented at previous Bled Workshops [24-26]. While the pionic effects on the nucleon mass appear reasonable, the analogous treatment of the A does not yet enhance especially its n-decay width enough in order to make it compatible with the relatively large phenomenological value [26]. Further ingredients appear to be necessary. We are presently in the course of extending the coupled-channels theory accordingly.
Acknowledgment
The authors are grateful to Bojan Golli, Mitja Rosina, and Simon Sirca for their continuous efforts of organizing every year the Bled Mini-Workshops. These meetings serve as a valuable institution of exchanging ideas and of mutual learning among an ever growing community of participating colleagues engaged in hadronic physics.
This work was supported by the Austrian Science Fund, FWF, through the Doctoral Program on Hadrons in Vacuum, Nuclei, and Stars (FWF DK W1203-N16).
References
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2.	L. Y. Glozman, Z. Papp, W. Plessas, K. Varga and R. F. Wagenbrunn, Phys. Rev. C 57, 3406 (1998)
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5.	J. P. Day, K. S. Choi, and W. Plessas, Few-Body Syst. 54, 329 (2013)
6.	J. P. Day, W. Plessas, and K. S. Choi, in: Looking into Hadrons (Proceedings of the MiniWorkshop, Bled, Slovenia, 2013), ed. by B. Golli, M. Rosina, and S. Sirca. DMFA, Ljubljana (2013); p. 6
7.	J. P. Day, PhD Thesis, University of Graz (2013)
8.	W. Plessas, in: Quark Masses and Hadron Spectra (Proceedings of the Mini-Workshop, Bled, Slovenia, 2014), ed. by B. Golli, M. Rosina, and S. Sirca. DMFA, Ljubljana (2014); p. 34
Resonances in the Constituent-Quark Model
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9. M. Rosina, in: Quark Masses and Hadron Spectra (Proceedings of the Mini-Workshop, Bled, Slovenia, 2014), ed. by B. Golli, M. Rosina, and S. Sirca. DMFA, Ljubljana (2014); p. 50
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16.	K. S. Choi and W. Plessas, Few-Body Syst. 54,1055 (2013)
17.	L. Y. Glozman, M. Radici, R. F. Wagenbrunn, S. Boffi, W. Klink, and W. Plessas, Phys. Lett. B 516,183 (2001)
18.	S. Boffi, L. Y. Glozman, W. Klink, W. Plessas, M. Radici, and R. F. Wagenbrunn, Eur. Phys. J. A 14, 17 (2002)
19.	T. Melde, L. Canton, and W. Plessas, Phys. Rev. Lett. 102,132002 (2009)
20.	T. Melde, W. Plessas, and R. F. Wagenbrunn, Phys. Rev. C 72, 015207 (2005); ibid. C 74, 069901 (2006)
21.	B. Sengl, T. Melde, and W. Plessas, Phys. Rev. D 76, 054008 (2007)
22.	T. Melde, W. Plessas, and B. Sengl, Phys. Rev. C 76, 025204 (2007)
23.	R. Kleinhappel, W. Plessas, and W. Schweiger, Few-Body Syst. 54, 339 (2013)
24.	R. Kleinhappel, W. Plessas, and W. Schweiger, in: Understanding Hadron Spectra (Proceedings of the Mini-Workshop, Bled, Slovenia, 2011), ed. by B. Golli, M. Rosina, and S. Sirca. DMFA, Ljubljana (2011); p. 36
25.	R. Kleinhappel, W. Plessas, and W. Schweiger, in: Hadronic Resonances (Proceedings of the Mini-Workshop, Bled, Slovenia, 2012), ed. by B. Golli, M. Rosina, and S. Sirca. DMFA, Ljubljana (2012); p. 20
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102 Povzetki v slovenščini
Analitična zgradba neperturbativnih kvarkovih propagatorjev in mezonskih procesov
Dalibor Kekeza in Dubravko Klabučarb a Rugjer Boškovič Institute, Bijenička č. 54,10000 Zagreb, Croatia
b Physics Department, Faculty of Science, Zagreb University, Bijenička č. 32, Zagreb 10000, Croatia
Raziskujemo analitično zgradbo nekaterih nastavkov za kvarkove propagatorje v neperturbativnem področju kromodinamike. Ce izberemo fizikalno motivirano parametrizacijo masne funkcije M(p2) oblečenih kvarkov, odvisne od gibalne količine in z določeno analitično zgradbo, je skrajno tezavno napovedati in obvladati analitično zgradbo ustreznega neperturbativnega kvarkovega propagatorja. Tudi problem Wickove rotacije, ki povezuje izrazavo v prostoru Minkowskega in Evklida, je skrajno tezaven v neperturbativnem območju. Izpeljemo obliko propagatorja, ki omogoča Wickovo rotacijo in dopusča enakovredne račune v prostoru Minkowskega in Evklida. Kljub preprostosti nudi ta model dober kvalitativen in semikvantitativen opis nekaterih pročesov z psevdoskalarnimi mezoni.
Primerjava med mezoni in resonancami WLWL pri energijah več TeV
Antonio Dobadoa, Rafael L. Delgadoa, Felipe J. Llanes-Estradaa and Domenec Espriub
a Dept. Fisica Teorica I, Univ. Complutense, 28040 Madrid
b Institut de Ciencies del Cosmos (ICCUB), Marti Franques 1, 08028 Barcelona, Spain.
Mikavni signali z Velikega hadronskega trkalnika (LHC) namigujejo, da morda obstajajo v področju zloma elektro-sibke simetrije resonance v območju več TeV. Spomnimo na nekajključnih resonanc mezon-mezon v območju GeV, ki bi utegnile imeti analogne resonance pri visokih energijah in nam sluzijo za primerjavo, hkrati z odgovarjujočo unitarizirano efektivno teorijo. Ceprav je podrobna dinamika lahko različna, pa zahteve po unitarnosti, kavzalnosti in globalnem zlomu simetrije (z uporabo metode inverzne amplitude) dovoljujejo prenos intuicije v večinoma neizmerjeno območje visokih energij. Ce bo povečano stevilo dogodkov na ATLASU okrog 2 TeV podprlo tako novo resonančo, to lahko pomeni anomalno sklopitev qqW.
Resonance v konstituentnem kvarkovem modelu.
R. Kleinhappel and W. Plessas
Theoretical Physics, Institute of Physics, University of Graz, A-8010 Graz, Austria
Na kratko poročamo o danasnjem opisu barionskih resonanc v realističnem modelu s konstituentnimi kvarki, v katerem običajno obravnavamo resonance kot
Povzetki v slovenščini 103
vzbujena vezana stanja, in pokaZemo pot do boljrealistične teorije, v kateri nastopijo resonance kot kompleksni poli v ravnini gibalna količina/energija, torejz realno maso in končno sirino.
Racun vzbujenih resonanc mezona p in faznih premikov nn v P-valu z razSirjenim kvarkovim modelom
Susana Coitoa, George Ruppb in Eef van Beverenc a Institute of Modern Physics, CAS, Lanzhou 730000, China
b CeFEMA, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal c Centro de F'isica Computacional, Departamento de F'isica, Universidade de Coimbra, 3004-516 Coimbra, Portugal
Raziskujemo vektorsko resonanco p(770), njene radialne ponovitve ter ustrezne fazne premike nn v P-valu z razsirjenim kvarkovim modelom, ki vsebuje tudi pare mezonov in pare qq. Pri tem upostevamo vse vazne razpadne kanale: psevdo-skalar-psevdoskalar, vektor- psevdoskalar, vektor-vektor, vektor-skalar, aksialni vektor-psevdoskalar in aksialni vektor-vektor, skupaj26 kanalov. Dva model-ska parametra sta dolocena s prejšnjimi vrednostmi, trije pa iz resonance p in nizkoenergijskih faznih premikov nn v P-valu. Zacasni rezultati ze nakazujejo sposobnost modela, da reproducira te fazne premike ter maso in sirino mezona p. Vendar rastejo fazni premiki pri visjih energijah prestrmo. Mozno zdravilo je vkljucitev resonanc v koncnih stanjih v vecini kanalov. Raziskava se nadaljuje.
Prispevek pionskega oblaka k elektromagnetni strukturi nukleona
D. Kupelwieser and W. Schweiger
Institute of Physics, University of Graz, A-8010 Graz, Austria
V tem prispevku nadaljujemo in razsirimo prejšnje racune elektro-sibkih oblikovnih faktorjev hadronov z uporabo tockovne oblike relativisticne kvantne mehanike. Posebejse zanimamo za pionske ucinke na elektromagnetno zgradbo nukleona. V ta namen uporabimo hibridni model s konstituentnimi kvarki, ki vsebuje poleg trojice valencnih kvarkov se komponento 3q+n. S preprosto valovno funkcijo za konfiguracijo 3q dobimo smiselne rezultate za oblikovne faktorje nukleona. V skladu z drugimim avtorji ugotovimo, da je ucinek pionov znaten le pod Q2 < 0.5 GeV2.