QCD Crossover at Low Temperatures from Lee-Yang Edge Singularity

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.