Abstract
For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory-based computations of the equation of state. Recently, a new resummation scheme was proposed [S. Mondal, S. Mukherjee, and P. Hegde, Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions, Phys. Rev. Lett. 128, 022001 (2022).] for such an expansion that resums contributions of correlation functions of conserved currents to all orders in the chemical potential. Here, we study the efficacy of this resummation scheme using a low energy model, namely the mean-field quark-meson model. After adapting the scheme for a mean-field analysis, we confront the results of this scheme with the direct solution of the model at finite density as well as compare with results from Taylor expansions. We study to what extent the two methods capture the analytical properties of the equation of state in the complex chemical potential plane. As expected, the Taylor expansion breaks down as soon as the baryon chemical potential reaches the radius of convergence defined by the Yang-Lee edge singularity. Encouragingly, the resummation not only captures the location of the Yang-Lee edge singularity accurately, but is also able to describe the equation of state for larger chemical potentials beyond the location of the edge singularity for a wide range of temperatures.
Highlights
Uncovering the structure of the phase diagram of quantum chromodynamics at nonzero temperature and density has been the central goal for both the theoretical and the experimental nuclear physic community
For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory-based computations of the equation of state
This directly translates into a mean-field thermodynamic potential with nontrivial, in general nonanalytic, dependence on the chemical potential
Summary
Uncovering the structure of the phase diagram of quantum chromodynamics at nonzero temperature and density has been the central goal for both the theoretical and the experimental nuclear physic community (see Ref. [1] for a review). In numerous theories, including QCD, the presence of a finite chemical potential in the Dirac operator gives rise to a. In addition to improved convergence, zeros of the partition function of QCD at imaginary μ have been identified, which could be related to physical singularities of the thermodynamic potential. The main motivation of this work is to examine this in detail regarding the analytic and thermodynamic properties of a model where these quantities can be computed directly To this end, we use a quark-meson model which can be solved directly in mean-field approximation.
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