Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion

TL;DR

This paper introduces a resummation method for the Taylor expansion of the QCD equation of state at finite baryon chemical potential, improving convergence and understanding of the sign problem in lattice QCD calculations.

Contribution

The authors develop a novel resummation scheme based on correlation functions to extend the applicability of Taylor expansions in lattice QCD thermodynamics.

Findings

Resummation improves convergence of the Taylor series.

Resummed partition function reflects zeros and sign problem severity.

Method generalizes to include temperature and quark mass resummations.

Abstract

Taylor expansion in powers of baryon chemical potential ($\mu_B$) is an oft-used method in lattice QCD to compute QCD thermodynamics for $\mu_B>0$. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of $\mu_B$ where such an expansion around $\mu_B=0$ can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in $\mu_B$ that is based on the $n$-point correlation functions of the conserved current ($D_n$). The method resums the contributions of the first $N$ correlation function $D_1,\dots,D_N$ to the Taylor expansion of the QCD partition function to all orders in $\mu_B$. We show that the resummed partition function is an approximation to the reweighted partition function at $\mu_B\ne0$. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on $32^3\times8$ lattices and for temperatures $T\approx145$-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of our scheme to include resummation of powers of temperature and quark masses in addition to $\mu_B$, and show that the alternative expansion scheme of [S. Bors\'anyi et al., Phys. Rev. Lett. 126, 232001 (2021).] is a special case of this generalized resummation.