Quantitative sum rule analysis of low-temperature spectral functions

TL;DR

This paper investigates how low-temperature pion gases affect QCD and Weinberg sum rules using spectral functions derived from chiral-mixing, revealing temperature-dependent deviations and the importance of pion mass corrections.

Contribution

It introduces a model-independent approach to analyze in-medium spectral functions and their impact on sum rules, incorporating recent vacuum spectral data and pion mass effects.

Findings

Weinberg sum rules remain valid at high temperatures.

QCD sum rules show significant deviations above ~140 MeV.

Pion mass corrections are crucial for accurate analysis.

Abstract

We analyze QCD and Weinberg-type sum rules in a low-temperature pion gas using vector and axial-vector spectral functions following from the model-independent chiral-mixing scheme. Toward this end we employ recently constructed vacuum spectral functions with ground and first-excited states in both channels and a universal perturbative continuum; they quantitatively describe hadronic tau-decay data and satisfy vacuum sum rules. These features facilitate the implementation of chiral mixing without further assumptions, and lead to in-medium spectral functions which exhibit a mutual tendency of compensating resonance and dip structures, suggestive for an approach toward structureless distributions. In the sum rule analysis, we account for pion mass corrections, which turn out to be significant. While the Weinberg sum rules remain satisfied even at high temperatures, the numerical evaluation of the QCD sum rules for vector and axial-vector channels reveals significant deviations setting in for temperatures beyond ~140 MeV, suggestive of additional physics beyond low-energy chiral pion dynamics.