The critical line from imaginary to real baryonic chemical potentials in two-color QCD

TL;DR

This paper tests the analytic continuation method for studying the critical line in two-color QCD at finite chemical potential, finding it to be analytic near zero but requiring high precision at imaginary values for accurate predictions.

Contribution

The study provides a direct validation of the analytic continuation method in two-color QCD, highlighting its limitations and the need for high precision at imaginary chemical potentials.

Findings

The critical line is analytic around 

High precision at imaginary  is necessary for accurate real  predictions

The method's validity is confirmed in the studied regime

Abstract

The method of analytic continuation from imaginary to real chemical potentials $\mu$ is one of the few available techniques to study QCD at finite temperature and baryon density. One of its most appealing applications is the determination of the critical line for small $\mu$: we perform a direct test of the validity of the method in this case by studying two-color QCD, where the sign problem is absent. The (pseudo)critical line is found to be analytic around $\mu^2 = 0$, but a very large precision would be needed at imaginary $\mu$ to correctly predict the location of the critical line at real $\mu$.