Consistent parameter fixing in the quark-meson model with vacuum fluctuations

Abstract

We revisit the renormalization prescription for the quark-meson model in an extended mean-field approximation, where vacuum quark fluctuations are included. At a given cutoff scale the model parameters are fixed by fitting vacuum quantities, typically including the sigma-meson mass mσ and the pion decay constant fπ. In most publications the latter is identified with the expectation value of the sigma field, while for mσ the curvature mass is taken. When quark loops are included, this prescription is however inconsistent, and the correct identification involves the renormalized pion decay constant and the sigma pole mass. In the present article we investigate the influence of the parameter-fixing scheme on the phase structure of the model at finite temperature and chemical potential. Despite large differences between the model parameters in the two schemes, we find that in homogeneous matter the effect on the phase diagram is relatively small. For inhomogeneous phases, on the other hand, the choice of the proper renormalization prescription is crucial. In particular, we show that if renormalization effects on the pion decay constant are not considered, the model does not even present a well-defined renormalized limit when the cutoff is sent to infinity.

Heavy quark diffusion in a Polyakov loop plasma

“…Appendix A: Polyakov loop extended Quark Meson modelPolyakov loop extended quark meson model(PQM) captures two important features of quantum chromodynamics(QCD) -namely chiral symmetry breaking and its restoration at high temperature and/densities as well as the confinement -deconfinement transitions. Explicitly, the Lagrangian of the PQM model is given by[37][38][39][40][41] …”

Inhomogeneous chiral condensate in the quark-meson model

“…To be specific, we focus on a chiral-density wave (CDW). The problem of inhomogeneous phases has been addressed before in the context of the Ginzburg-Landau approach [16][17][18][19], the NJL [20][21][22][23][24][25] and PNJL models [26,27], the QM model [22,28,29], and the nonlocal chiral quark model [30]. Numerical methods for the calculation of the phase diagram for a general inhomogeneous condensate are available [31,32], but we resort to a chiral-density wave ansatz in order to present analytical results.…”

Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking

“…This turns out to be true in our model as well, at least up to quadratic-order fluctuations. For m σ and f π it was shown in reference [21] that it is crucial to fit the pole mass and to take into account the renormalization of the pion wave function, corresponding to the pole of D σ and the residue of D π , respectively. The resulting expressions are (see Refs.…”

“…Likewise F (m σ,0 ) means that the function L 2 ((iω m , q)) is analytically continued to the real time-like momentum q = (m σ,0 , 0). The explicit expressions can be found in reference [21].…”