Dynamical Local Chirality and Chiral Symmetry Breaking

TL;DR

This paper investigates how spontaneous chiral symmetry breaking in QCD is reflected in local chiral properties of Dirac eigenmodes, introducing a correlation measure to describe this phenomenon and identifying a relevant dynamical scale.

Contribution

It introduces the correlation coefficient of polarization C_A as a new tool to analyze local chirality and links chiral symmetry breaking to the dominance of correlated modes over anti-correlated modes.

Findings

Correlated modes exhibit local chirality preference.

Anti-correlated modes favor anti-chirality.

Identification of a chiral polarization scale Lambda_ch.

Abstract

We present some of the reasoning and results substantiating the notion that spontaneous chiral symmetry breaking (SChSB) in QCD is encoded in local chiral properties of Dirac eigenmodes. Such association is possible when viewing chirality as a dynamical effect, measured with respect to the benchmark of statistically independent left-right components. Following this rationale leads to describing local chiral behavior by a taylor-made correlation, namely the recently introduced correlation coefficient of polarization C_A. In this language, correlated modes (C_A>0) show dynamical preference for local chirality while anti-correlated modes (C_A<0) favor anti-chirality. Our conclusion is that SChSB in QCD can be viewed as dominance of low-energy correlation (chirality) over anti-correlation (anti-chirality) of Dirac sea. The spectral range of local chirality, chiral polarization scale Lambda_ch, is a dynamically generated scale in the theory associated with SChSB. One implication of these findings is briefly discussed.