On the three-point order parameters of chiral symmetry breaking

TL;DR

This paper investigates nonlocal three-point Green functions related to chiral symmetry breaking in QCD using Resonance chiral theory, matching high-energy constraints and lattice data, with applications to muon g-2 and pion decay.

Contribution

It introduces an extended Resonance chiral theory framework to accurately describe three-point correlators and match multiple high-energy QCD constraints.

Findings

Correlators expressed in closed form with minimal resonance extension

Parameters constrained by lattice data

Implications for muon g-2 and pion decay processes

Abstract

The nonlocal order parameters of the QCD chiral symmetry breaking, namely the nonanomalous three-point Green functions of the quark bilinears belonging to the odd intrinsic parity sector, are studied within the framework of the Resonance chiral theory. The general form of these correlators is then matched with various high energy constraints: the leading and sub-leading OPE for all three momenta simultaneously large, the leading OPE for two momenta large and the leading and sub-leading Brodsky-Lepage limit for the corresponding transition form factor. In order to satisfy these constraints, the Resonance chiral theory has to be enlarged with additional resonance multiplets and with higher derivative operators as well. We discuss a minimal extension of this kind in detail and present corresponding correlators in a closed form. The remaining free parameters are then constrained from lattice data. As a phenomenological application, we discuss the pion-pole contribution to the muon $g-2$ and the decay $\pi^0\to e^+e^-$.