M. K. Volkov

Effective hadron theory of QCD

Abstract We review present path-integral attempts to derive effective meson-baryon Lagrangians out of QCD or QCD-motivated quark models. There exist two different approaches to the solution of this problem for mesons. In the first case mesons are treated as composite quark-antiquark objects, whereas in the second case they are introduced as chiral phase of quark fields and external sources in the QCD Lagrangian. Our main attention is devoted to a discussion of the more dynamical first approach. This includes the hadronization of the Nambu-Jona-Lasinio model and various physical applications of the resulting effective Lagrangian concerning strong, electromagnetic and weak interactions of mesons. There emerge basically two principally different types of effective hadron theories reflecting the alternative (but at the same time dual) pictures of baryons: baryons as chiral (topological) solitons of the meson fields and as bound states of quarks and diquarks. It is demonstrated that these two pictures describe only two sides of the same medal.

EXCITED PIONS, ρ- AND ω-MESONS AND THEIR DECAYS IN A CHIRAL SU(2) × SU(2) LAGRANGIAN

A chiral SU(2) × SU(2) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the Nambu–Jona-Lasinio (NJL) quark model with separable nonlocal interactions, with form factors corresponding to three-dimensional ground and excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pions, ρ-and ω-mesons are described with the help of two form factors. The weak decay constant Fπ′ is calculated. The values for the decay widths of the processes ρ→2π, π′→ρπ, ρ′→2π, ρ′→ωπ and ω′→ρπ are obtained in agreement with the experimental data.

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric dense color superconducting phase of a Nambu-Jona-Lasinio-type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.

MESONS AND DIQUARKS IN A NJL MODEL AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

An extended NJL model with and (qq)-interactions is studied at finite temperature and baryon number density. We investigate the chiral symmetry breaking, its restoration and the behavior of meson and diquark masses, decay and coupling constants as functions of T and µ.

Nonlocal Polyakov–Nambu–Jona-Lasinio model beyond mean field and the QCD phase transition

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1/Nc correction to the quark condensate is carefully studied and compared with the usual local Nambu-Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. The model is also applied to finite temperature. We find that the 1/Nc corrections dominate the melting of the chiral condensate at low temperatures, T<100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1/Nc corrections in the cross-over regime depends on the parameter T0 of the Polyakov loop potential. For T0=270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase transition temperature in comparison with the mean-field result. Near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme is needed to include mesonic correlations in that regime. Lowering T0 leads to a more rapid cross-over even at the mean-field level and the unstable region for the 1/Nc corrections shrinks. For T0< 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.

Excess low-energy photon pairs from pion annihilation at the chiral phase transition

Abstract The photon pair production by pion annihilation in a hot and dense medium at the chiral phase transition is investigated within a chiral quark model. As a direct consequence of this transition the σ meson appears as a bound state in the domain of temperatures and chemical potentials where the condition M σ (T,μ)≈2 M π (T,μ) is fulfilled. This effect results in a strong enhancement of the cross section for the pion annihilation process 2π→2γ compared with the vacuum case. The calculation of the photon pair production rate as function of the invariant mass shows a strong enhancement and narrowing of the σ meson resonance at threshold due to chiral symmetry restoration.

QCD-motivated Nambu-Jona-Lasinio model with quark and gluon condensates

Abstract We present a systematic study of the role of the nonperturbative gluon condensate arising in a QCD-motivated NJL model. The effects of the gluon condensate on induced meson couplings, the pion decay constant, quark condensate and mass formulae are investigated. An interesting result is the change of the scale Λ of chiral symmetry breaking and of the universal four-quark coupling ϰ .

1/ N c expansion of the quark condensate at finite temperature

Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic 1/{ital N}{sub {ital c}} expansion. Using a general separable ansatz for the nonlocal interaction, we derive a self-consistent equation for the 1/{ital N}{sub {ital c}} correction to the quark propagator. For a separable model with cutoff form factor, we obtain a decrease of the condensate of the order of 20{percent} at zero temperature. A lowering of the critical temperature for the onset of the chiral restoration transition due to the inclusion of mesonic correlations is obtained with results that seem to be closer to those from lattice calculations. {copyright} {ital 1996 The American Physical Society.}

Pion polarizability in chiral quantum field theory

Abstract The amplitude for the process γγ → ππ is calculated in the chiral quantum field theory. The values α π (±) = 0.3 α/m π 3 and α π (0) = −0.04 α/m π 3 are found for the pion polarizabilities.

Scalar mesons in the Nambu-Jona-Lasinio model with the ’t Hooft interaction

SummaryWe calculate the mass spectra of the pseudoscalar and scalar meson nonets in the Nambu-Jona-Lasinio model with the ’t Hooft interaction. We obtain satisfactory result for the pseudoscalar mesons. For the scalar mesons, the ’t Hooft interaction somewhat increases the values of the masses. However, it is not sufficient to explain the whole scalar mass spectrum. The situation could be improved for the φ and f0 mesons through mixing with the glueball state. For the description of the masses of a0 and K0* mesons, it is necessary to involve other models. The strong decay widths of scalar mesons are described.