Another mean field treatment in the strong coupling limit of lattice QCD

TL;DR

This paper introduces a new mean field approach based on next-to-leading order large dimensional expansion to study the QCD phase diagram in the strong coupling limit, aiming to reconcile mean field results with MDP simulations.

Contribution

It proposes a novel auxiliary field related to point-splitting mesonic composites, improving mean field predictions of the QCD phase boundary shape in the strong coupling limit.

Findings

Shifted transition temperature aligns better with expectations.

Improved phase boundary shape compared to previous mean field results.

Effects are larger than those observed in MDP simulations.

Abstract

We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresponds to the point-splitting mesonic composite. Fermion determinant with this mean field under the anti-periodic boundary condition gives rise to a term which interpolates the effective potentials in the previously proposed zero and finite temperature mean field treatments. While the shift of the transition temperature at zero chemical potential is in the desirable direction and the phase boundary shape is improved, we find that the effects are too large to be compatible with the MDP simulation results.