Generalized susceptibilities of net-baryon number based on the 3-dimensional Ising universality class

TL;DR

This study explores the critical behavior of high-order susceptibilities of net-baryon number in QCD by mapping from the 3D Ising model, revealing characteristic patterns near the critical point.

Contribution

It introduces a detailed analysis of high-order net-baryon susceptibilities using the 3D Ising universality class, including sub-leading effects and their impact on observable patterns.

Findings

Negative dips and positive peaks in susceptibilities near the critical point

Robustness of positive peak structure as a signature of criticality

Sub-leading contributions modify susceptibility density plots

Abstract

Assuming the equilibrium of the QCD system, we have investigated the critical behavior of sixth-, eighth- and tenth-order susceptibilities of net-baryon number, through mapping the results in the three-dimensional Ising model to that of QCD. Both the leading critical contribution as well as sub-leading critical contribution from the Ising model are discussed. When considering only the leading critical contribution, the density plots for susceptibilities of the same order demonstrate a consistent general pattern independent on values of mapping parameters. As the critical point is approached from the crossover side, a negative dip followed by a positive peak is observed in the $\mu_B$ dependence of the three different orders of susceptibilities. When sub-leading critical contribution is taken into account, modifications become apparent in the density plots of the susceptibilities. The emergence of negative dips in the $\mu_B$ dependence of the susceptibilities is not an absolute phenomenon, while the positive peak structure is a more robust feature of the critical point.