A. E. Radzhabov

Effects of mesonic correlations in the QCD phase transition

The finite-temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above Tc the pressure is well described by the mean-field-approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed.

σ meson in hot and dense matter

An important role of the scalar isoscalar σ meson in low-energy physics is discussed. The behavior of the σ meson in a hot and dense medium is studied. It is shown that, in the vicinity of the critical values of the temperature (T) and the chemical potential (μ), the σ meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes ππ → γγ and ππ → ππ near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and the phase transition of hadron matter into quark-gluon plasma take place.

Two-photon decays of vector mesons and dilepton decays of scalar mesons in dense matter

Two-photon decays of vector mesons and dilepton decays of scalar mesons, which are forbidden in vacuum and can occur in dense baryonic matter due to the explicit violation of Lorentz symmetry, are described within a quark model of the Nambu–Jona-Lasinio type. The temperature and chemical potential dependence of these processes is investigated. It is found that their contribution to the production of photons and leptons in heavy-ion collisions is enhanced near the conditions corresponding to the restoration of chiral symmetry. Moreover, in the case of the a0-meson and especially the ρ-meson, a resonant behaviour (an additional amplification) is observed due to the degeneration of ρ and a0 masses when hot hadron matter approaches a chirally symmetric phase.

SU(2)×SU(2) chiral quark model with nonlocal interaction

Masses and interactions of light mesons are described in the framework of the model with the chiral invariant SU(2)×SU(2) four-quark interaction. The nonlocal kernel of the interaction is chosen in the form that ensures the absence of ultraviolet divergences in the Feynman diagrams and poles in the quark propagator. Within this model, we demonstrate that, in the chiral limit, the pion mass equals zero and the Goldberger-Treiman relation is fulfilled. The sigma-meson mass and the widths of strong decays σ → ππ, ρ → νν are estimated.

Process γ*γ → σ at large virtuality of γ*

The process gamma* gamma ->sigma is investigated in the framework of the SU(2)xSU(2) chiral NJL model. The form factor of the process is derived for arbitrary virtuality of gamma* in the Euclidean kinematic domain. The asymptotic behaviour of this form factor resembles the asymptotic behaviour of the gamma* gamma ->pi form factor.The process γ*γ → σ is investigated in the framework of the SU(2)×SU(2) chiral NJL model. The form factor of the process is derived for arbitrary virtuality of γ* in the Euclidean kinematic domain. The asymptotic behavior of this form factor resembles the asymptotic behavior of the γ*γ → π form factor.

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. It is found that the 1/Nc corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/Nc expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.

ρ(ω) → π 0 π 0 γ, ρ(ω) → ηπ 0 γ decays in the local quark Nambu-Jona-Lasinio model

The branching ratios and photon spectra of the rare processes ρ(ω) → π0π0γ, ρ(ω) → ηπ0γ are calculated in the framework of the standard local quark Nambu-Jona-Lasinio model. Three types of diagrams are considered: the quark box and the pole diagrams with scalar (σ, α0(980)) and vector (ρ, ω) mesons. The obtained estimates for the widths of the processes ρ(ω) → π0π0γ are in satisfactory agreement with existing experimental data. Predictions are made for the widths of the processes ρ(ω) → ηπ0γ.

ππ scattering in a nonlocal chiral quark model

We consider a nonlocal version of the Nambu and Jona-Lasinio model with the SU(2) × SU(2) chiral symmetry broken by the current-quark-mass term. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favor of the values of the pion mass mπ, the pion decay constant fπ, and the current quark mass mc. It is shown that, in the model, the main low-energy theorems which are known for pions are fulfilled. The s-, p-, and d-wave scattering lengths in all isotopic channels and the s-wave slope parameters are calculated, and the results are in satisfactory agreement with phenomenological data.

In-medium modification of meson properties in a chiral quark model

Two-photon decays of vector mesons and dilepton decays of scalar mesons which are forbidden in a vacuum and can occur in dense baryonic matter due to the explicit violation of Lorentz symmetry are described within a quark model of the Nambu-Jona-Lasinio type. The temperature and chemical potential dependence of these processes is investigated.