Improved Measure of Local Chirality

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.