QCD sum rules for rho mesons in vacuum and in-medium, re-examined

TL;DR

This paper re-examines QCD sum rules for rho mesons in vacuum and medium, emphasizing the importance of chiral symmetry breaking scale and clarifying the reliability of low moments versus higher moments.

Contribution

It provides a refined analysis of rho meson spectral moments, highlighting the validity of low moments and the limitations of higher moments in QCD sum rule applications.

Findings

Low moments allow accurate sum rule analysis with controlled inputs.

Higher moments are unreliable due to uncertainties in higher-dimensional condensates.

Factorization approximation for four-quark condensates is invalid in studied cases.

Abstract

An updated investigation of QCD sum rules for the first two moments of rho meson spectral functions, both in vacuum and in-medium, is performed with emphasis on the role of the scale related to spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral distributions do permit an accurate sum rule analysis with controlled input including QCD condensates of the lowest dimensions, whereas higher moments are subject to uncertainties from higher dimensional condensates. Possible connections with Brown-Rho scaling are discussed. The factorization approximation for four-quark condensates is shown not to be applicable in any of the cases studied.