# Pion radiative weak decay from the instanton vacuum

## TL;DR

This paper calculates the vector and axial-vector form factors for pion radiative weak decays using the instanton vacuum model, finding good agreement with experimental data and analyzing their momentum transfer dependence.

## Contribution

It introduces a calculation of pion radiative weak decay form factors within the instanton vacuum framework, including nonlocal effects and their impact on form factor values.

## Key findings

- Vector form factor enhanced by ~20% due to nonlocal effects
- Axial-vector form factor reduced by ~30% due to nonlocal effects
- Results agree well with experimental data at zero momentum transfer

## Abstract

We investigate the vector and axial-vector form factors for the pion radiative weak decays $\pi^+\to e^+\nu_e \gamma$ and $\pi^+\to e^+\nu_e e^+ e^-$, based on the gauged effective chiral action from the instanton vacuum in the large $N_c$ limit. The nonlocal contributions, which arise from the gauging of the action, enhance the vector form factor by about $20\,\%$, whereas the axial-vector form factor is reduced by almost $30\,\%$. Both the results for the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The dependence of the form factors on the momentum transfer is also studied. The slope parameters are computed and compared with other works.