https://doi.org/10.1140/epja/s10050-023-01098-1
Letter
From imaginary to real chemical potential QCD with functional methods
1
Institut für Theoretische Physik, Justus-Liebig-Universität Gießen, 35392, Gießen, Germany
2
Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Gießen, 35392, Gießen, Germany
b
christian.fischer@theo.physik.uni-giessen.de
Received:
9
May
2023
Accepted:
26
July
2023
Published online:
8
August
2023
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 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.125.052001. arXiv:2002.02821 [hep-lat], 2020). We find that the analytically continued crossover line agrees very well (within one percent) with the explicitly calculated one for chemical potentials up to about 80 % of the one of the critical end point. The method breaks down in the region where the chiral susceptibility as a function of the condensate cannot any longer be well described by a polynomial.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.