From imaginary to real chemical potential QCD with functional methods

We investigate the quality of the extrapolation procedure employed in Ref. [1] to extract the crossover line at real chemical potential from lattice data at imaginary potential. To this end we employ a functional approach that does not suffer from the sign problem. We utilize a well-studied combination of lattice Yang–Mills theory with a truncated set of Dyson–Schwinger equations in Landau gauge for $$2 + 1$$ quark flavors. This system predicts a critical endpoint at moderate temperatures and rather large (real) chemical potential with a curvature of the pseudo-critical transition line comparable to recent lattice extrapolations. We determine the light quark condensate and chiral susceptibility at imaginary chemical potentials and perform an analytic continuation along the lines described in Borsányi et al. (Phys Rev Lett 125:052001. https://doi.org/10.1103/PhysRevLett.125.05200