Chiral condensates in massless QCD and the $U(1)_A$ boson mass

TL;DR

This paper calculates the mass of the $U(1)_A$ boson in massless QCD using vacuum condensates and anomaly effects, providing a numerical estimate relevant for understanding chiral symmetry breaking.

Contribution

It introduces a method to determine the $U(1)_A$ boson mass from vacuum condensates and anomaly considerations in massless three-flavor QCD, with a specific numerical result.

Findings

$U(1)_A$ boson mass estimated at 310±50 MeV

Mass derived from mixed quark-gluon condensate and anomaly

Supports the role of vacuum structure in chiral symmetry breaking

Abstract

The $U(1)_A$ boson mass is calculated through the phenomenological characteristics of the vacuum related to spontaneous breaking of chiral symmetry in QCD. The mass is determined by the mixed quark-gluon condensate $\langle \bar q G q \rangle$ that emerges in an appropriate correlation function due to triangle anomaly. For three flavor QCD in chiral limit we find the numerical value for the $U(1)_A$ boson mass to be $M_0=310\pm 50~{\rm MeV}$.