QCD Crossover at Low Temperatures from Lee-Yang Edge Singularity

TL;DR

The paper addresses charting the QCD crossover into the low-temperature, high-baryon-density regime and constraining the location of a possible critical endpoint. It introduces a universality-driven approach that combines Lee–Yang edge singularity analysis with chiral scaling to map imaginary-$\mu_B$ lattice data to the real $T$–$\mu_B$ plane, enabling a first-principles estimate of the chiral crossover line at $T\simeq 108$ MeV without relying on small-$\mu_B$ expansions. Using (2+1)-flavor lattice simulations at imaginary $\mu_B$ and $T\approx 107.71$ MeV, the leading Lee–Yang edge is extracted from baryon-number susceptibilities, and the edge is connected to the scaling variable via a mapping function $g$ constrained by the edge condition. The reconstructed crossover band, consistent across two volumes and two mapping forms, aligns with established low-density results and heavy-ion freeze-out, and shows no evidence for a CEP at this temperature within the studied discretizations, suggesting any CEP would lie at lower $T$; the method provides a robust, extensible framework for mapping the QCD phase diagram at low $T$ and high $\mu_B$.

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 $μ_B$ with universal chiral scaling to determine the $μ_B$ 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 $μ_B$ with a single lattice spacing and two volumes, we compute $μ_B$-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 $\{T,μ_B\}$ and the scaling variable (\textit{i.e.}\ the argument of the universal scaling functions). This mapping function then yields the $μ_B$ 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-$μ_B$ expansion, the resulting $μ_B$ dependence of the pseudo-critical temperature is consistent with established lattice-QCD determinations at small $μ_B$ 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-$μ_B$ regime.

Figures (8)

• Figure 1: Fits to lattice data using the regular-plus-singular ansatz \ref{['eq:singular']}. Filled points: $20^{3}\times10$; open points: $32^{3}\times10$ (only $\chi_1^B$). Differences between data and regular background are shown for both volumes.
• Figure 2: Scatter plot of the Lee--Yang edge locations in the complex $\mu_B$ plane. Left: $20^{3}\times10$ lattices with $\chi_1^B$-$\chi_4^B$. Middle: $20^{3}\times10$ lattices with only $\chi_1^B$. Right: $32^{3}\times10$ with only $\chi_1^B$. Crosses and ellipses show cluster medians and $1\sigma$ regions from Gaussian mixture model clustering.
• Figure 3: Reconstructed chiral crossover lines from the $20^{3}\!\times\!10$ ensemble (red band) and the $32^{3}\!\times\!10$ ensemble (blue band). In each case the solid curve inside the band denotes the median reconstruction, and the band shows the central 68% bootstrap interval (16th--84th percentiles). Results from previous lattice QCD computations HotQCD:2018pdsBorsanyi:2020fev and freeze-out results from experiments Cleymans:2005xv are also shown.
• Figure 4: Comparison of the reconstructed crossover line using the elliptic and polynomial mapping functions. Left: Both mappings applied to the $20^{3}\times 10$ lattice data. Middle: Elliptic mapping applied to $20^{3}\times 10$ and $32^{3}\times 10$ lattices. Right: polynomial mapping applied to the same two lattice volumes. The lower subplot in each panel shows the ratio of the central value of the crossover temperature from this work to that determined by the HotQCD collaboration using the Taylor expansion method at nonzero $\mu_B$HotQCD:2018pds.
• Figure 5: Same as \ref{['fig:muBc_posterior']} but obtained using the lower bound $\mu_{B,\text{min}}=$ 400 MeV (top) and 450 MeV (bottom).