Quark Number Fluctuations at Finite Temperature and Finite Chemical Potential via the Dyson-Schwinger Equation Approach

TL;DR

This paper studies quark number fluctuations at finite temperature and chemical potential using Dyson-Schwinger equations, identifying critical points and analyzing model dependencies.

Contribution

It provides a detailed analysis of higher-order quark number fluctuations near the critical end point using Dyson-Schwinger equations with different gluon models.

Findings

Fluctuations diverge at the critical end point.

Second order fluctuation shows a clear peak at CEP.

Location of CEP shifts with model parameters.

Abstract

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Marris-Tandy (MT) model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and forth order fluctuations of net quark number all diverge at the critical end point (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the MT model and the Qin-Chang model, we give the pseudo-critical temperature at zero quark chemical potential as $T_{c}=146$ MeV and $150$ MeV, and locate the CEP at $({\mu_{E}^{q}}, {T_{E}^{}}) = (120, 124)$ MeV and $(124,129)$ MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.