Pion-to-photon transition distribution amplitudes in the non-local chiral quark model

TL;DR

This paper employs a non-local chiral quark model to compute pion-to-photon transition distribution amplitudes, providing nonperturbative inputs crucial for understanding pion annihilation processes and comparing theoretical predictions with experimental data.

Contribution

It introduces a non-local chiral quark model framework that ensures polynomiality of TDAs and explores the effects of non-locality on symmetry properties and form factors.

Findings

Vector TDA symmetry is broken in the non-local model.

Calculated transition form factors agree with experimental parametrizations.

Residual dependence on the cut-off function form is observed.

Abstract

We apply the non-local chiral quark model to study vector and axial pion-to-photon transition amplitudes that are needed as a nonperturbative input to estimate the cross section of pion annihilation into the real and virtual photon. We use a simple form of the non-locality that allows to perform all calculations in the Minkowski space and guaranties polynomiality of the TDA's. We note only residual dependence on the precise form of the cut-off function, however vector TDA that is symmetric in skewedness parameter in the local quark model is no longer symmetric in the non-local case. We calculate also the transition form-factors and compare them with existing experimental parametrizations.