Chiral and U_A(1) symmetry in correlation functions in medium

TL;DR

This review explores how chiral and U_A(1) symmetry breaking effects manifest in correlation functions within medium, linking theoretical formulas to observable phenomena like the eta' mass.

Contribution

It provides a comprehensive overview of the role of symmetry breaking in correlation functions and discusses the implications for meson masses in medium environments.

Findings

Chiral symmetry breaking is linked to the density of zero eigenvalues via the Banks-Casher formula.

U_A(1) breaking effects are associated with topologically non-trivial configurations depending on flavor number.

The Witten Veneziano formula relates the eta' mass to topological susceptibility in medium.

Abstract

In this review, we will discuss how the chiral symmetry and U_A(1) breaking effects are reflected in the correlation functions. Using the Banks-Casher formula, one can identify the density of zero eigenvalues to be the common ingredient that governs the chiral symmetry breaking in correlation functions between currents composed of light quarks with or without a heavy quark. Similarly the presence of the U_A(1) breaking effect is determined through the contribution of the topologically non trivial configurations that depends on the number of flavors. We also discuss how the symmetry breaking effects are reflected in the gluon correlation functions. Finally, we review the Witten Veneziano formula for the eta' mass in medium.