Improved Measure of Local Chirality

TL;DR

This paper challenges previous interpretations of local chirality measurements in QCD vacuum studies, showing that observed double-peaking is a phase-space artifact and proposing a new universal X parameter to better detect genuine QCD effects.

Contribution

It introduces a new universal definition of the local chirality parameter that removes phase-space effects, clarifying the interpretation of chirality distributions in QCD vacuum analysis.

Findings

Double-peaking in X-distribution is a phase-space effect.

The new X parameter yields a uniform distribution for random fields.

The traditional double peak disappears with the new definition.

Abstract

It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears.