SU(2) Yang-Mills theory in (1 + 1) dimensions: A finite-lattice approach

Finite-lattice methods are used to calculate the masses of the lowest-lying baryon and meson states in the two-dimensional SU(2) Yang-Mills theory. No sign of a phase transition is seen at non-zero quark mass m. Both the meson and baryon mass vanish at m = 0: this is presumably a “chiral protection” mechanism.     

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.     

ΔB = −ΔL, neutron →e−π+, e−K+, μ−π+ and μ−K+ decay modes in SU(2)L × SU(2)R × SU(4)col or SO(10)

It is stressed that within the simplest model SU(4) of color, unifying quarks with leptons, where B  L is a gauge symmetry, a spontaneous breaking of this symmetry leads naturally to baryonlepton decays like n→e^?k⁺, e^?K⁺, μ^?π⁺, μ^?K⁺ [in constant to SU(5) where B  L is not gauged]. Our mechanism is crucially tied to the presence of the Higgs multiplet (2, 2, 15) of SU(2) × SU(2) × SU(4), which is needed to account for the observed quarklepton mass ratios.     

Baryon masses in the broken chiral quark bag

We consider corrections to the baryon mass spectrum when the u and the d quarks are massive, i.e. the pion acquires its physical mass. This breaks explicitely the SU(2) chiral symmetry of the chiral quark model. We also include the massive K- and η-mesons to examine the broken SU(3) and SU(3) × SU(3) symmetries. These small corrections do improve the mass spectrum.     

Chiral soliton model vs. pentaquark structure for Θ(1540)

The exotic baryon Θ⁺(1540 MeV) is visualized as an expected (iso) rotational excitation in the chiral soliton model. It is also argued as a pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast these two points of view; observe the similarities and differences between the two pictures. Collective excitation, the characteristic of chiral soliton model, points toward small mixing of representations in the wake ofSU (3) breaking. In contrast, constituent quark models prefer near ‘ideal’ mixing, similar to ω-φ mixing.     

Baryon masses in large N c chiral perturbation theory

We analyse the baryon mass spectrum in a framework which combines the 1/N _c expansion with chiral perturbation theory. Meson loop contributions involving the full SU(3) octet of pseudoscalar Goldstone bosons are evaluated, and the influence of explicit chiral and flavor symmetry breaking by non-zero and unequal quark masses is investigated. We also discuss sigma terms and the strangeness contribution to the nucleon mass. Received: 29 June 1998 / Revised version: 25 November 1998     

Heavy to light baryon weak form factors in the lightcone constituent quark model

Heavy to light baryon weak form factors are investigated in a lightcone constituent quark model. In a SU(4) symmetry broken scheme, both charged and neutral weak current-induced form factors are calculated at theq ² = 0 point including the leading relativistic effects in the spin composition of baryons. The corresponding semileptonic decays are described by assuming dipole dependence of form factors onq ².     

Strangeness, charm, and bottom in a chiral quark-meson model

In this paper, we investigate an SU(3) extension of the chiral quark-meson model. The spectra of baryons with strangeness, charm, and bottom are considered within a “rigid oscillator” version of this model. The similarity between the quark sector of the Lagrangian in the model and the Wess-Zumino term in the Skyrme model is noted. The binding energies of baryonic systems with baryon numbers B=2 and 3 possessing strangeness or heavy flavor are also estimated. The results are in good qualitative agreement with those obtained previously in the chiral soliton (Skyrme) model.     

Magnetic moments of the strange baryons in the bag model

We break SU(3) symmetry in the bag model by giving the singlet quark a mass m. The magnetic moment ratios of the strange baryons are calculated and compared with exact SU(6) predictions and with experiment.     

Spontaneous breaking of global baryon number symmetry

We study the possibility that theU(1) _B global symmetry associated with baryon number is spontaneously broken. We present realistic examples implemented in the context of a suitably extended standardSU(2) _L×U(1)×SU(3)_c model and of a composite model of quarks and leptons. The globalU(1) _B symmetry in both cases is spontaneously broken at a relatively low mass scale without any conflict with observations. The dominant baryon number nonconserving process in these models obeys the ΔB=2 selection rule.     

Thermodynamic properties of the SU(2)f chiral quark–loop soliton

We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)_f Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and δ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed. Received: 26 September 1997     

Pentaquarks in chiral soliton models

The spectra of pentaquarks, some of them observed recently, are discussed within the topological soliton model and compared with the simplified quark picture. The results obtained within the chiral soliton model depend to some extent on the quantization scheme: rigid rotator, soft rotator, or bound state model. The similarity of the spectra of baryon resonances obtained within the quark model and the chiral soliton model is pointed out, although certain differences take place as well, which require careful interpretation. In particular, considerable variation of the strange antiquark mass in different SU(3) multiplets of pentaquarks is required to fit their spectra obtained from chiral solitons. Certain difference in the masses of “good” and “bad” diquarks is required as well, in qualitative agreement with previously made estimates. The partners of exotic states with different values of spin which belong to higher SU(3) multiplets have energy considerably higher than the states with the lowest spin, and this could be a point where the difference from simple quark models is striking. The antiflavor excitation energies for multibaryons are estimated as well, and the binding energies of gJ-hypernuclei and anticharm (antibeauty) hypernuclei are presented for several baryon numbers. Some deficiencies are pointed out in the arguments in the literature against the validity of the chiral soliton approach and/or the SU(3) quantization models. Based partly on the talks presented at the International Seminar on High Energy Physics Quarks-2004, Pushkinogorie, Russia, May 24–30, 2004; International Workshop on Quantum Field Theory and High Energy Physics QFTHEP-04, Saint-Petersburg, Russia, June 17–23, 2004, and Symposium of London Mathematical Society “Topological Solitons and their Applications,” Durham, UK, August 2–12, 2004. A slightly reduced version of this paper is available as E-print HEP-PH/0507028. The text was submitted by the author in English.     

Solitons in the Nambu-Jona-Lasinio model with vector and axial mesons

We study the effect of vector and axial isovector mesons in the soliton of the SU(2) NJL-model for static hedgehog configurations and on the chiral circle. The Lagrangian reproduces Sakurai's Universality and implements vector dominance through current-field identities. The parameters of the Lagrangian are fixed by means of a heat-kernel expansion up to second order taking theA-π mixing into account. For the corresponding set of parameters we find solitons for constituent quark masses betweenM～265–345 MeV which are much lower than those found without vector mesons. For the valueM=315 MeV which corresponds both to the KSFR relation 2g _ρ ² f _π ² =m _ρ ² and the Weinberg sum rule m _A ² =m _ρ ² the soliton has a clearly negative quark eigenvalue. The soliton mass is about 1100 MeV. For this choise of parameters the radius and axial coupling constant turn out to be too small.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

Baryon bound state in two-dimensional SU(N) gauge theory

The bound-state baryon problem with N quarks in an SU(N) gauge model of strong interactions is investigated in one-space and one-time dimensions. A study of planar diagrams yields color singlet “baryon” states of quarks that have infrared divergence-free mass spectra. The resulting integral equation turns out to be identical to the one obtained in a particular string model.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Binding energy of the dihyperon in the quark cluster model

The dihyperon is described in the non-relativistic quark cluster model. The SU(3) flavor symmetry breaking due to the different quark masses is taken into account not only in the hamiltonian, but also in the quark wave functions. The interaction contains the one-gluon-exchange potential, pseudoscalar-meson exchange between quarks plus an additional phenomenological σ-meson exchange. The mass of the dihyperon is predicted to be (2211 ± 5) MeV, i.e. a binding energy of the dihyperon of (−20 ± 5) MeV below the ΛΛ threshold is found.     

The effects of SU(3) breaking in the CERN-bag model

Introducing SU(3) breaking via the mass of the strange quark, the ratios of one-particle distributions are calculated in the central region. The agreement with the experimental data is good.     

Relativistic corrections to the baryon resonance photoexcitation amplitudes in the quark model

We calculate the relativistic corrections of order (quark mass)^?2 to the baryon resonance photoexcitation amplitudes in the harmonic-oscillator quark model. We find that the relativistic effects entail significant consequences and that the agreement with experiment is much improved.