Ultraviolet asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory

TL;DR

This paper calculates the short-distance and high-frequency asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory at 2-loop order, providing refined Wilson coefficients and insights relevant for lattice comparisons.

Contribution

It provides the first detailed 2-loop order analysis of correlator asymptotics in hot Yang-Mills theory, refining Wilson coefficients and highlighting convergence issues.

Findings

Refined Wilson coefficients for correlators

Discrepancies with previous literature identified

Potential implications for lattice data interpretation

Abstract

Inspired by recent lattice measurements, we determine the short-distance (a << r << 1/pi T) as well as large-frequency (1/a >> omega >> pi T) asymptotics of scalar (trace anomaly) and pseudoscalar (topological charge density) correlators at 2-loop order in hot Yang-Mills theory. The results are expressed in the form of an Operator Product Expansion. We confirm and refine the determination of a number of Wilson coefficients; however some discrepancies with recent literature are detected as well, and employing the correct values might help, on the qualitative level, to understand some of the features observed in the lattice measurements. On the other hand, the Wilson coefficients show slow convergence and it appears uncertain whether this approach can lead to quantitative comparisons with lattice data. Nevertheless, as we outline, our general results might serve as theoretical starting points for a number of perhaps phenomenologically more successful lines of investigation.