QCD Crossover at Low Temperatures from Lee-Yang Edge Singularity

TL;DR

This paper introduces a novel lattice-QCD method combining Lee-Yang edge analysis with universal chiral scaling to estimate the QCD crossover line at low temperatures and high baryon chemical potential, providing new insights into the phase diagram.

Contribution

The authors develop a new approach that uses Lee-Yang edge singularities and universal scaling to determine the QCD critical line at low temperatures from lattice simulations.

Findings

Estimated the QCD crossover line down to 108 MeV.

Validated the method against known lattice-QCD results at small μ_B.

Demonstrated compatibility with heavy-ion collision freeze-out parameters.

Abstract

We provide the first lattice-QCD estimate of the crossover line down to $T\simeq108$~MeV. We introduce a new method that combines the Lee-Yang edge in the complex plane of baryon chemical potential $\mu_B$ with universal chiral scaling to determine the $\mu_B$ dependence of the QCD chiral critical and pseudo-critical temperatures. By performing $(2\!+\!1)$-flavor lattice QCD simulations at $T\simeq108$~MeV and purely imaginary $\mu_B$ with a single lattice spacing and two volumes, we compute $\mu_B$-dependent baryon-number susceptibilities and extract the location of the Lee-Yang edge. Together with universal scaling near the QCD chiral transition, it constrains the mapping function between $\{T,\mu_B\}$ and the scaling variable (\textit{i.e.}\ the argument of the universal scaling functions). This mapping function then yields the $\mu_B$ dependence of the critical and pseudo-critical temperatures for $T\gtrsim108$~MeV. While our calculation is performed only at a single value of low temperature without explicit input from small-$\mu_B$ expansion, the resulting $\mu_B$ dependence of the pseudo-critical temperature is consistent with established lattice-QCD determinations at small $\mu_B$ and compatible with chemical freeze-out parameters of heavy-ion collisions down to low temperatures, demonstrating the validity and robustness of the method. Application of this method can be systematically extended to additional temperatures and finer discretizations, opening a pathway to charting the QCD phase diagram in the low-$T$, high-$\mu_B$ regime.