Distribution of Canonical Determinants in QCD

TL;DR

This paper uses chiral perturbation theory to analyze the distribution of canonical determinants in QCD, revealing complex values, moments, and their cancellations, with comparisons to lattice data and a log-normal distribution model.

Contribution

It provides a detailed analytical study of the distribution and moments of canonical determinants in QCD, including complex value behavior and cancellation effects, validated against lattice data.

Findings

Canonical determinants are complex-valued for non-zero quark charge.

The distribution of the magnitude follows a log-normal distribution.

Significant cancellation occurs between real and imaginary parts.

Abstract

The distribution of canonical determinants in QCD is determined by means of chiral perturbation theory. For a non-zero quark charge the canonical determinants take complex values. In the dilute pion gas approximation, we compute all moments of the magnitude of the canonical determinants, as well as the first nonvanishing moments of the real and imaginary parts. The non-trivial cancellation between the real and the imaginary parts of the canonical determinants is derived and the signal to noise ratio is discussed. The analytical distributions are compared to lattice data. The average density of the magnitude of the canonical determinants is determined as well and is shown to be given by a variant of the log-normal distribution.