Chiral matrix model of the semi-Quark Gluon Plasma in QCD

Abstract

A chiral matrix model applicable to QCD with 2+1 flavors is developed. This requires adding a SU(3)_L x SU(3)_R x Z(3)_A nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y. Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. In addition to the usual symmetry breaking term, linear in the current quark mass m_qk, at a nonzero temperature T it is necessary to add a new term, ~ m_qk T^2. The parameters of the gluon part of the matrix model are identical to that for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, eta, and eta'. The temperature for the chiral crossover at T_chi = 155 MeV is determined by adjusting the Yukawa coupling y. We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent beta - 1. We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the chi_2n. Especially sensitive tests are provided by chi_4 - chi_2 and by chi_6, which changes in sign about T_chi. The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from T_chi, that the transition to deconfinement is significantly quicker than indicated by the measurements of the (renormalized) Polyakov loop on the lattice.