L. Ya. Glozman

THE SPECTRUM OF THE NUCLEONS AND THE STRANGE HYPERONS AND CHIRAL DYNAMICS

Abstract The spectra of the nucleons, Δ resonances and the strange hyperons are well described by the constituent quark model if in addition to the harmonic confinement potential the quarks are assumed to interact by exchange of the SU (3) F octet of pseudoscalar mesons, which are the Goldstone bosons associated with the hidden approximate chiral symmetry of QCD. In its SU (3) F invariant approximation the pseudoscalar exchange interaction splits the multiplets of SU (6) FS × U (6) conf in the spectrum to multiplets of SU (3) F × SU (2) S × U (6) conf . The position of these multiplets differs in the baryon sectors with different strangeness because of the mass splitting of the pseudoscalar octet and the different constituent masses of the u , d and s quarks that breaks SU (3) F flavor symmetry. A description of the whole spectrum, to an accuracy of − 4% or better, is achieved if one matrix element of the boson interaction for each oscillator shell is extracted from the empirical mass splittings. The ordering of the positive and negative parity states moreover agrees with the empirical one in all sectors of the spectrum. A discussion of the conceptual basis of the model and its various phenomenological ramifications is presented.

Unified description of light- and strange-baryon spectra

We present a chiral constituent quark model for light and strange baryons providing a unified description of their ground states and excitation spectra. The model relies on constituent quarks and Goldstone bosons arising as effective degrees of freedom of low-energy QCD from the spontaneous breaking of chiral symmetry. The spectra of the three-quark systems are obtained from a

Restoration of chiral and U(1)A symmetries in excited hadrons

Abstract The effective restoration of SU ( 2 ) L × SU ( 2 ) R and U ( 1 ) A chiral symmetries of QCD in excited hadrons is reviewed. While the low-lying hadron spectrum is mostly shaped by the spontaneous breaking of chiral symmetry, in the high-lying hadrons the role of the quark condensate of the vacuum becomes negligible and the chiral symmetry is effectively restored. This implies that the mass generation mechanisms in the low- and high-lying hadrons are essentially different. The fundamental origin of this phenomenon is a suppression of quark quantum loop effects in high-lying hadrons relative to the classical contributions that preserve both chiral and U ( 1 ) A symmetries. Microscopically the chiral symmetry breaking is induced by the dynamical Lorentz-scalar mass of quarks due to their coupling with the quark condensate of the vacuum. This mass is strongly momentum-dependent, however, and vanishes in the high-lying hadrons where the typical momentum of valence quarks is large. This physics is illustrated within the solvable chirally symmetric and confining model. Effective Lagrangians for the approximate chiral multiplets at the hadron level are constructed which can be used as phenomenological effective field theories in the effective chiral restoration regime. Different ramifications and implications of the effective chiral restoration for the string description of excited hadrons, the decoupling of excited hadrons from the Goldstone bosons, the glueball—quark–antiquark mixing and the OZI rule violations are discussed.

Parity doublets and chiral symmetry restoration in baryon spectrum

Abstract It is argued that an appearance of the near parity doublets in the upper part of the light baryon spectrum is an evidence for the chiral symmetry restoration in the regime where a typical momentum of quarks is around the chiral symmetry restoration scale. At high enough baryon excitation energy the nontrivial gap solution, which signals the chiral symmetry breaking regime, disappears and the chiral symmetry should be restored. Thus one observes a phase transition in the upper part of the light baryon spectrum. The average kinetic energy of the constituent quarks in this region is just around the critical one 3 T c .

Θ+ in a chiral constituent quark model and its interpolating fields

Abstract The recently discovered pentaquark Θ + is described within the chiral constituent quark model. Within this picture the flavor-spin interaction between valence quarks inverts the (1 s ) 4 and (1 s ) 3 (1 p ) levels of the four-quark subsystem and consequently the lowest-lying pentaquark is a positive parity, I =0, J =1/2 state of the flavor antidecuplet, similar to the soliton model prediction. Contrary to the soliton model, however, the quark picture predicts its spin-orbit partner with J =3/2. Different interpolating fields intended for lattice calculations of Θ + are constructed, which have a maximal overlap with this baryon if it is indeed a quark excitation in the 5 Q system.

Light baryons in a constituent quark model with chiral dynamics

Abstract It is shown from rigorous three-body Faddeev calculations that the masses of all 14 lowest states in the N and Δ spectra can be described within a constituent quark model with a Goldstone-boson-exchange interaction plus linear confinement between the constituent quarks.

Chiral multiplets of excited mesons

Abstract It is shown that experimental meson states with spins J =0,1,2,3 in the energy range 1.9–2.4 GeV obtained in a recent partial wave analysis of proton–antiproton annihilation at LEAR remarkably confirm all predictions of chiral symmetry restoration. Classification of excited q q mesons according to the representations of chiral U (2) L × U (2) R group is performed. There are two important predictions of chiral symmetry restoration in highly excited mesons: (i) physical states must fill out approximately degenerate parity-chiral multiplets; (ii) some of the physical states with the given I , J PC are members of one parity-chiral multiplet, while the other states with the same I , J PC are members of the other parity-chiral multiplet. For example, while some of the excited ρ (1,1 −− ) states are systematically degenerate with a 1 (1,1 ++ ) states forming (0,1)+(1,0) chiral multiplets, the other excited ρ (1,1 −− ) states are degenerate with h 1 (0,1 +− ) states ((1/2,1/2) chiral multiplets). Hence, one of the predictions of chiral symmetry restoration is that the combined amount of a 1 (1,1 ++ ) and h 1 (0,1 +− ) states must coincide with the amount of ρ (1,1 −− ) states in the chirally restored regime. It is shown that the same rule applies (and experimentally confirmed) to many other meson states.

Chiral symmetry restoration and the string picture of hadrons

Abstract QCD string picture of highly excited hadrons very naturally explains parity doubling once the chiral symmetry is restored high in the spectrum. In particular, the spin–orbit and tensor interactions of quarks at the ends of the string, related to dynamics of the string, vanish. High in the spectrum there appears higher degree of degeneracy, namely parity doublets with different angular momentum cluster around energy of the string in the given quantum state.

SU(2)L×SU(2)R and U(1)A restorations high in the hadron spectrum and what it tells us about

Abstract Recent data for highly excited mesons suggest that not only the chiral SU (2) L × SU (2) R symmetry of QCD is restored high in the spectrum but also the U (1) A symmetry. This means that it is not a confining interaction in QCD which triggers the spontaneous breaking of chiral symmetry. The restoration of the U (2) L × U (2) R symmetry of the QCD Lagrangian implies the appearance of multiplets of this group high in the hadron spectra. Such type of multiplets is naturally explained within the string picture of confinement. It also supports the scenario that the U (1) A breaking is related to instantons and not to the gluonic interaction responsible for confinement.

The Baryon baryon interaction in a modified quark model

Abstract The quark-cluster model with coupling constants constraint by chiral symmetry is extended to include strange quarks. In this model, besides the confinement and one-gluon exchange potentials, the pseudoscalar mesons and sigma (σ) meson exchanges are included as the nonperturbative effect. Using this interaction we studied the binding energy of the deuteron, the NN scattering phase shifts and the hyperon-nucleon cross sections in the framework of the resonating group method (RGM). The results are reasonably consistent with experiments.