Baryon number probability distribution at finite temperature

TL;DR

This paper investigates the probability distribution of net baryon number at finite temperature using the functional renormalization group, revealing Z(3) symmetry effects and computing cumulants consistent with susceptibilities.

Contribution

It demonstrates the impact of Z(3) symmetry on baryon number states and links probability distributions with generalized susceptibilities at finite temperature.

Findings

States with fractional baryon number are prohibited due to Z(3) symmetry.

Cumulants of baryon number distribution match generalized susceptibility results.

The probability distribution provides insights into color confinement mechanisms.

Abstract

The probability distribution of the net baryon number is investigated within the functional renormalization group approach. We find that the Roberge-Weiss periodicity related to the Z(3) symmetry of the gluon fields results directly in that, states of the net baryon number $N_B=N\pm 1/3$ with $N\in\mathbb{Z}$ are prohibited, and only those of $N_B=N$ are possible. By employing the probability distribution of the net baryon number, we also compute the cumulants of the baryon number distribution, which are found to be well consistent with those obtained from the generalized susceptibilities. A question about the relation between the color confinement and the probability distribution of net baryon number is put forward.