Equation of state for cold and dense heavy QCD

TL;DR

This paper extends an effective lattice theory for heavy QCD at low temperatures and high densities, analyzing its validity, addressing lattice saturation effects, and deriving an analytical solution that agrees with numerical simulations to compute the cold nuclear equation of state.

Contribution

It advances the effective theory for heavy QCD by including higher-order terms and demonstrates an analytical solution method unaffected by the sign problem, providing a continuum-extrapolated equation of state.

Findings

Effective theory extended to order ~u^5κ^8.

Lattice saturation effects identified and addressed.

Analytical linked cluster expansion agrees with simulations.

Abstract

A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order $\sim u^5\kappa^8$ in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.