Baryon susceptibilities, non-Gaussian moments, and the QCD critical point

Abstract

We calculate model-independently the impact of the critical point on higher-order baryon susceptibilities ${\ensuremath{\chi}}_{n}$, showing how they depend on fluctuations of the order parameter. We characterize the kurtosis of the order parameter fluctuations and the baryon moments ${\ensuremath{\chi}}_{3},{\ensuremath{\chi}}_{4}$ as functions on the phase diagram. Important features of this analysis are then confirmed by a Gross--Neveu model study with good qualitative agreement with other model studies. We also compare this to lattice and experimental data. Our results support the universality of the characteristic peak in baryon susceptibilities as a signal of the critical point. We discuss leveraging measurements of different ${\ensuremath{\chi}}_{n}$ to extrapolate the location of the critical point.