Thermal QCD sum rules in the $\rho^0$ channel revisited

TL;DR

This paper revisits thermal QCD sum rules in the $ ho^0$ channel, deriving scaling relations for scalar operators at low temperatures and analyzing the temperature dependence of the gluon condensate and $ ho$-meson mass.

Contribution

It introduces a new approach to thermal QCD sum rules based on a linear relation between the spectral threshold and the QCD scale, revealing a significant temperature dependence of the gluon condensate.

Findings

Gluon condensate shows sizable temperature dependence.

$ ho$-meson mass increases slowly with temperature.

Scaling relations for scalar operators are derived at low temperatures.

Abstract

From the hypothesis that at zero temperature the square root of the spectral continuum threshold $s_0$ is linearly related to the QCD scale $\Lambda$ we derive in the chiral limit and for temperatures considerably smaller than $\Lambda$ scaling relations for the vacuum parts of the Gibbs averaged scalar operators contributing to the thermal operator product expansion of the $\rho^0$ current-current correlator. The scaling with $\lambda\equiv \sqrt{s_0(T)/s_0(0)}$, $s_0$ being the $T$-dependent perturbative QCD continuum threshold in the spectral integral, is simple for renormalization group invariant operators, and becomes nontrivial for a set of operators which mix and scale anomalously under a change of the renormalization point. In contrast to previous works on thermal QCD sum rules with this approach the gluon condensate exhibits a sizable $T$-dependence. The $\rho$ -meson mass is found to rise slowly with temperature which coincides with the result found by means of a PCAC and current algebra analysis of the $\rho^0$ correlator.