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

Abstract

Taylor expansion in powers of baryon chemical potential (μ_{B}) is an oft-used method in lattice QCD to compute QCD thermodynamics for μ_{B}>0. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of μ_{B} where such an expansion around μ_{B}=0 can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in μ_{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},…,D_{N} to the Taylor expansion of the QCD partition function to all orders in μ_{B}. We show that the resummed partition function is an approximation to the reweighted partition function at μ_{B}≠0. 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}×8 lattices and for temperatures T≈145-176 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 scheme to include resummation of powers of temperature and quark masses in addition to μ_{B}, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).PRLTAO0031-900710.1103/PhysRevLett.126.232001] is a special case of this generalized resummation.

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