OPE-RchiT matching at order alpha_s: hard gluonic corrections to three-point Green functions

TL;DR

This paper advances the matching between QCD and resonance chiral theory at order alpha_s by computing relevant Green functions and addressing the inclusion of hadronic states for better theoretical consistency.

Contribution

It provides the first calculation of hard-gluon corrections to three-point Green functions in the OPE-RchiT matching at order alpha_s.

Findings

Computed two- and three-point Green functions in QCD and RchiT.

Identified the importance of including an infinite tower of hadronic states.

Clarified the role of non-analytic terms in the matching process.

Abstract

In this work we push the matching between the QCD operator product expansion (OPE) and resonance chiral theory (RchiT) to order alpha_s. To this end we compute two- and three-point QCD Green functions (GFs) in both theories and compare the results. GFs which are order parameters of chiral symmetry breaking make this matching more transparent and thus we concentrate on those. On the OPE side one needs to calculate the hard-gluon virtual corrections to the quark condensate, and in particular for three-point GFs this computation was hitherto missing. We also discuss the need for including the infinite tower of hadronic states in the hadronic representation of the GF when non-analytic terms such as logarithms are present in the OPE Wilson coefficients.