Effective Potential in the Strong-coupling Lattice QCD with Next-to-Next-to-Leading Order Effects

TL;DR

This paper derives an analytic effective potential in strong-coupling lattice QCD including NNLO effects, revealing how higher-order corrections influence phase transition points and order parameters at finite temperature and chemical potential.

Contribution

It provides the first systematic derivation of NNLO effects in the effective potential of lattice QCD, extending previous NLO analyses with detailed evaluation of connected plaquette configurations.

Findings

NNLO effects modify wave function renormalization, quark mass, and chemical potential.

Critical temperature and chemical potential are similar to NLO results.

Position of the critical point is sensitive to NNLO corrections.

Abstract

We derive an analytic expression of the effective potential at finite temperature (T) and chemical potential (mu) in the strong-coupling lattice QCD for color SU(3) including next-to-next-to-leading order (NNLO) effects in the strong coupling expansion. NNLO effective action terms are systematically evaluated in the leading order of the large dimensional (1/d) expansion, and are found to come from some types of connected two plaquette configurations. We apply the extended Hubbard-Stratonovich transformation and a gluonic dressed fermion technique to the effective action, and obtain the effective potential as a function of T, mu, and two order parameters; chiral condensate and a vector potential field. The next-to-leading order (NLO) and NNLO effects result in modifications of the wave function renormalization factor, quark mass and chemical potential. We find that T_{c,mu=0} and mu_{c,T=0} are similar to the NLO results, whereas the position of the critical point is sensitive to NNLO corrections.