The QCD deconfinement transition for heavy quarks and all baryon chemical potentials

TL;DR

This paper develops an effective three-dimensional lattice QCD theory for heavy quarks that captures deconfinement transition behavior across all baryon chemical potentials, enabling simulations despite the sign problem.

Contribution

It introduces a systematic derivation of an effective theory from thermal lattice QCD with heavy Wilson quarks, incorporating center symmetry and addressing the sign problem at finite chemical potentials.

Findings

Effective theory accurately describes deconfinement transition.

Sign problem can be mitigated via flux representation.

Critical end point determined across parameter space.

Abstract

Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_\tau\sim 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.