Universal Properties of Chiral Simmetry Breaking

TL;DR

This paper explores the critical phenomena of chiral symmetry breaking using theoretical tools like PCAC and correlation length scaling, providing methods to locate critical points and measure critical indices relevant to lattice QED and QCD.

Contribution

It introduces a scaling theory for the pion to sigma mass ratio and links PCAC with critical index measurement, advancing understanding of chiral phase transitions.

Findings

A scaling theory for $R_\pi$ ratio is developed.

PCAC and correlation length scaling relate pion mass to chiral condensate.

Practical methods for measuring the anomalous dimension $\eta$ are proposed.

Abstract

We discuss chiral symmetry breaking critical points from the perspective of PCAC, correlation length scaling and the chiral equation of state. A scaling theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The Goldstone character of the pion and properties of the longitudinal and transverse chiral susceptibilities determine the ratio $R_\pi$ which can be used to locate critical points and measure critical indices such as $\delta$. We show how PCAC and correlation length scaling determine the pion mass' dependence on the chiral condensate and lead to a practical method to measure the anomalous dimension $\eta$. These tools are proving useful in studies of the chiral transition in lattice QED and the quark-gluon plasma transition in lattice QCD.