Response functions of hot and dense matter in the Nambu-Jona-Lasino model

We investigate current-current correlation functions, or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics, namely mean-field theory and a beyond-mean-field theory, taking into account mesonic contributions. Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation, showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the self-energy or density-of-state contribution, and the Maki-Thompson contribution.Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to carefully treat the linear terms in external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities. These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.     

Possible Instability of the Ground State of Two-Flavour Colour Superconductor Induced by Colour Neutrality

The diquark condensate susceptibility in neutral colour superconductor at moderate baryon density is calculated in the frame of the two-flavour Nambu-Jona-Lasinio model with the mean field approximation. When colour chemical potential is introduced to keep charge neutrality, the dlquark condensate susceptibility ＆ negative in the directions without diquark condensate in colour space, which may be regarded as a signal of the instability of the conventional ground state with only diquark condensate in the colour-3 direction.     

Investigation of the tetraquark states ■ in the improved chromomagnetic interaction model

In the framework of the improved chromomagnetic interaction model, we complete a systematic study of the S-wave tetraquark states ■ ( Q = c, b, and q = u, d, s) with different quantum numbers: J^PC= 0⁽+(+)), 1⁽+(±)),and 2⁽+(+)). The mass spectra of tetraquark states are predicted, and the possible decay channels are analyzed by considering both the angular momentum and C-parity conservation. The recently observed hidden-charm tetraquark states with stra...