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  • Open Access

Bulk viscosity of quark matter across the QCD phase transitions

Chong-long Xie, Guo-yun Shao*, Ming-zheng-xuan Wu, and Wei-bo He

  • MOE Key Laboratory for Non-equilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China

  • *Contact author: gyshao@mail.xjtu.edu.cn
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Phys. Rev. C 113, 045213 – Published 28 April, 2026

DOI: https://doi.org/10.1103/yp8h-pdkr

Abstract

Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity (ζ) and its ratio to shear viscosity (ζ/η) of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the 2+1 flavor Polyakov-loop improved Nambu–Jona-Lasinio model. We explore the behaviors of specific bulk viscosity (ζ/s) and ζ/η across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both ζ/s and ζ/η are extremely small at high temperatures, approaching the nature of a conformal theory. Larger ζ/s and ζ/η are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, ζ/s and ζ/η generally increase with decreasing temperature, though ζ/η exhibits a slight decline near the critical end point. On the boundary of the first-order transition, ζ/s shows a nonmonotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both ζ/s and ζ/η, with magnitudes even exceeding those near the chiral crossover of u,d quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.

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Phys. Rev. C 113, 045213– Published 28 April, 2026
  • Received 19 December 2025
  • Revised 4 March 2026
  • Accepted 1 April 2026
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