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Analytic structure of the QCD phase diagram in the complex-temperature plane

Gökçe Başar*

Vladimir V. Skokov†

  • *Contact author: gbasar@unc.edu
  • †Contact author: vskokov@ncsu.edu
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Phys. Rev. D 114, 034516 – Published 24 August, 2026

DOI: https://doi.org/10.1103/vkhk-9dx8

Abstract

We study the analytic structure of the QCD phase diagram by treating temperature as a complex variable. The nearest Yang-Lee edge singularities in the complex-T plane bound the domain of analyticity of temperature-dependent thermodynamic observables and complement the more commonly studied singularities in the complex chemical-potential plane. Our analysis combines three complementary perspectives: universal critical scaling, a first-principles extraction from lattice-QCD data, and explicit illustrations in effective models. We illustrate the resulting structure in a random-matrix model and in a quark-meson model, where the singularity trajectories can be followed explicitly. At small real chemical potential, the leading complex-temperature singularity admits an analytic expansion in μ2, while near a critical point it crosses over to the universal Puiseux form dictated by Ising critical scaling. We show that the complex-T and complex-μ trajectories are controlled by the same scaling variables and mapping coefficients, so their comparison provides a stringent consistency test of critical-point searches and constrains the extent of the critical scaling regime. Finally, we analyze lattice-QCD data at μ=0 using an iterated conformal-Padé approach and extract the continuum location of the nearest complex-temperature singularity. The result is consistent with the expectation that, at physical quark masses, the real part of the leading singularity lies between the chiral-limit transition temperature and the physical-mass chiral-susceptibility peak temperature, while its imaginary part remains nonzero.

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Phys. Rev. D 114, 034516– Published 24 August, 2026
  • Received 23 June 2026
  • Accepted 12 August 2026
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