Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

Mukherjee, Swagato; Rennecke, Fabian; Skokov, Vladimir V.

doi:10.1103/PhysRevD.105.014026

Title: Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

Journal Article · Wed Jan 26 00:00:00 EST 2022 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.105.014026· OSTI ID:1842222

;

; Skokov, Vladimir V.

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, in arXiv:2106.03165, a new resummation scheme was proposed 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 solvable 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.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704; SC0020081

OSTI ID:: 1842222

Alternate ID(s):: OSTI ID: 1842810

Report Number(s):: BNL-222688-2022-JAAM; PRVDAQ; 014026

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 105 Journal Issue: 1; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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