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
1
Institute of Modern Physics, Northwest University, 710127, Xi’an, China
2
Frankfurt Institute for Advanced Studies, 60438, Frankfurt am Main, Germany
Received:
22
September
2022
Accepted:
23
January
2023
Published online:
4
February
2023
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 
field) in the equilibrium case and dynamical phase transition, respectively. By setting the system size to the typical size of the QGP fireball (
fm
), 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 
of the 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 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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
