Anomalies and discrete chiral symmetries

TL;DR

This paper explores how quantum anomalies affect discrete chiral symmetries in QCD, linking residual symmetries to the strong CP problem and analyzing phase transitions related to the theta parameter.

Contribution

It clarifies the role of discrete chiral symmetries in QCD with massive quarks and their connection to the strong CP-violating parameter theta, including implications for flavor extrapolation.

Findings

First order transition at theta = pi for degenerate light quarks.

Residual discrete symmetry relates to the strong CP problem.

Framework clarifies validity of rooting prescription in flavor extrapolation.

Abstract

The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.