The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy

Lijia Jiang; Horst Stöcker; Jun-Hui Zheng

doi:10.1140/epjc/s10052-023-11261-z

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 117
https://doi.org/10.1140/epjc/s10052-023-11261-z

Regular Article - Theoretical Physics

The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy

Lijia Jiang¹, Horst Stöcker² and Jun-Hui Zheng¹^c

¹ Institute of Modern Physics, Northwest University, 710127, Xi’an, China
² Frankfurt Institute for Advanced Studies, 60438, Frankfurt am Main, Germany

^c junhui.zheng@nwu.edu.cn

Received: 22 September 2022
Accepted: 23 January 2023
Published online: 4 February 2023

Abstract

By linearly parameterizing the QCD Landau free energy near the critical point in the baryon chemical potential and temperature plane, we study the fluctuations of the QCD chiral order parameter field (the $σ$ $\sigma$ field) in the equilibrium case and dynamical phase transition, respectively. By setting the system size to the typical size of the QGP fireball ( $\approx 10^{3}$ $\approx 10^3$ fm $^{3}$ $$^3$$ ), we show that in the equilibrium case, the discontinuity of the order parameter in the first order phase transition region is replaced by smooth crossover, and the corresponding fluctuations are broadened. Meanwhile, the quartic cumulant $κ_{4}$ $\kappa _4$ of the $σ$ $\sigma$ field is generally negative near the phase transition line. We further derive the dynamical evolution of the QCD Landau free energy in the Fokker–Plank framework, based on which we deduce the dynamical cumulants of the $σ$ $\sigma$ field. Assuming the temperature decreases as a known function of time, we numerically evaluate the dynamical cumulants and confirm that the cumulants present clear memory effects. Moreover, the memory effects on the first order phase transition side is stronger than that on the crossover side, and the dynamical cumulants at the hypothetical freeze-out line present rich non-monotonic structures.

© The Author(s) 2023

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