U_A(1) Anomaly at high temperature: the scalar-pseudoscalar splitting in QCD

TL;DR

This paper investigates the scalar-pseudoscalar correlation length splitting in high-temperature QCD, attributing it to instanton effects and analyzing its temperature dependence.

Contribution

It provides an estimate of the scalar-pseudoscalar splitting in high-temperature QCD due to instanton chains, highlighting its suppression at very high temperatures.

Findings

Splitting arises from instanton/anti-instanton chains in the thermal ensemble.

Splitting diminishes as temperature increases, vanishing asymptotically.

The suppression follows a power law proportional to (\Lambda_{QCD}/T)^b.

Abstract

We estimate the splitting between the spatial correlation lengths in the scalar and pseudoscalar channels in QCD at high temperature. The splitting is due to the contribution of the instanton/anti-instanton chains in the thermal ensemble, even though instanton contributions to thermodynamic quantities are suppressed. The splitting vanishes at asymptotically high temperatures as $\Delta M/M\propto (\Lambda_{QCD}/T)^b$, where $b$ is the beta function coefficient.