Two-Hadron Saturation for the Pseudoscalar-Vector-Vector Correlator and Phenomenological Applications

TL;DR

This paper constructs a pseudoscalar-vector-vector correlator using meson multiplets, constrains it with theoretical limits, and applies it to predict decay widths, achieving results consistent with experimental data within 2 sigma.

Contribution

It introduces a novel correlator model constrained by QCD and the Brodsky-Lepage limit, enabling precise predictions of meson decay processes.

Findings

Predicted decay widths agree with experimental data within 2 sigma.

The model provides a parameter-free prediction for the pion transition form factor.

Incorporating radiative corrections improves agreement with KTeV results.

Abstract

The pseudoscalar-vector-vector correlator is constructed using two meson multiplets in the vector and two in the pseudoscalar channel. The parameters are constrained by the operator product expansion at leading order where two or all three momenta are considered as large. Demanding in addition the Brodsky-Lepage limit one obtains (in the chiral limit) a pion-vector-vector correlator with only one free parameter. The singly virtual pion transition form factor and the decay width of omega to pion and photon are independent of this parameter and can serve as cross-checks of the results. The free parameter is determined from a fit of the omega-pion transition form factor. The resulting pion-vector-vector correlator is used to calculate the decay widths of omega to pion and dielectron and to pion and dimuon and finally the widths of the rare decay pion to dielectron and of the Dalitz decay pion to photon and dielectron. Incorporating radiative QED corrections the calculations of neutral-pion decays are compared to the KTeV results. We find a deviation of 2 sigma or less for the rare pion decay.