Lattice simulations of QCD with $\mu_B\neq0$ versus phase quenched QCD

TL;DR

This paper compares lattice QCD results at finite baryon chemical potential with phase quenched predictions, revealing the sign problem's physical significance and its relation to phase transition lines, and analyzing the applicability of Taylor expansions.

Contribution

It establishes a direct link between the sign problem's strength and the pion condensation transition line in phase quenched QCD, clarifying the limits of Taylor expansion methods.

Findings

Sign problem strength correlates with pion condensation transition line.

Number of Taylor expansion terms depends on the sign problem.

QCD phase transition endpoints are near phase quenched transition lines.

Abstract

Previously published lattice results for QCD at $\mu_B\neq0$ are compared to analytic predictions for phase quenched QCD. We observe that the strength of the sign problem in QCD is linked directly to the position of the phase transition line for pion condensation in phase quenched QCD and that the number of terms needed in the Taylor expansion approach depends on the strength of the sign problem. Together this emphasizes the physical importance of the sign problem and helps to clarify the range over which the Taylor expansion approach is practically applicable. Finally, we observe that the positions of the endpoint of the first order chiral phase transition in the QCD phase diagram found in two successive computations by Fodor and Katz are both close to the position of the phase transition line for pion condensation in phase quenched QCD.