Assessing the Reconstruction of the Critical Line in the QCD Phase Diagram from Imaginary to Real Chemical Potential

TL;DR

This study evaluates a lattice simulation technique for reconstructing the QCD phase boundary at real chemical potential from imaginary values, using the Quark-Meson model, and finds limitations near the critical endpoint.

Contribution

It provides a quantitative assessment of the reconstruction method’s validity range and highlights potential inaccuracies near the critical endpoint in the phase diagram.

Findings

Reconstruction technique valid up to about 146 MeV chemical potential.

Discrepancy of approximately 150% near the critical endpoint.

Reconstruction may not reliably locate the critical endpoint.

Abstract

We test a technique adopted in the lattice simulations framework, to reconstruct the chiral-phase boundary at real chemical potential, $\mu$, via extrapolation from imaginary $\mu$. We use a low-energy effective model, the Quark-Meson model, both in the mean-field approximation and within the Functional Renormalization Group, the latter in the Local Potential Approximation. The model provides results both for real and imaginary values of $\mu$, thus a direct comparison can be performed between the prediction of the model for real values of $\mu$ and the ones obtained via extrapolation from the results at imaginary $\mu$. We compute an effective convergence radius for the reconstruction technique, $\mu_\mathrm{conv}$, and find $\mu_\mathrm{conv}\approx146$ MeV. This value sustains the validity of the reconstruction technique also for finite and moderate values of the chemical potential. On the other hand, within our model, $\mu_\mathrm{conv}$ is quite smaller then the value of $\mu$ where we find the actual critical endpoint. Near this point of the phase diagram, we find a discrepancy between the actual phase boundary and the one pbtained via extrapolatin of $\approx150\%$. Therefore, our results show that the location of the critical endpoint obtained via reconstruction from imaginary $\mu$ should be considered with due caution