The Fluctuations of the Quark Number and of the Chiral Condensate

TL;DR

This paper investigates the complex fluctuations of quark number and chiral condensate in QCD at nonzero chemical potential, revealing the intricate cancellations affecting baryon number and condensate calculations.

Contribution

It provides the first leading order chiral perturbation theory analysis of the complex distributions of these operators in QCD at finite density.

Findings

Distributions are complex due to non-hermitian operators.

Sign problem causes distributions to be non-real and non-positive.

Insights into cancellations in baryon number and chiral condensate contributions.

Abstract

The distributions of the quark number and chiral condensate over the gauge fields are computed for QCD in Euclidean space at nonzero quark chemical potential. As both operators are non-hermitian the distributions are in the complex plane. Moreover, because of the sign problem, the distributions are not real and positive. The computations are carried out within leading order chiral perturbation theory and give a direct insight into the delicate cancellations that take place in contributions to the total baryon number and the chiral condensate.