# Transition form-factor of $\gamma\rightarrow 3\pi$ in nonlocal quark model

## TL;DR

This paper investigates the gamma to three pions transition form factor using a nonlocal chiral quark model, aligning with chiral perturbation theory and experimental data, highlighting the role of nonlocality and quark mass effects.

## Contribution

It introduces a nonlocal quark model to study the gamma to three pions transition form factor, extending previous local models and matching experimental results.

## Key findings

- Agreement with chiral perturbation theory in local limit
- Reproduction of Wess-Zumino-Witten anomaly
- Close match to experimental data at physical threshold

## Abstract

The transition form factor of a gamma into three pions $F_{3\pi}$ are studied in a framework of nonlocal chiral quark model. In local limit the result is agreement with chiral perturbative theory and reproduce Wess-Zumino-Witten anomaly. Availability of nonlocality not change a value of transition form factor in chiral limit. On the physical threshold of reaction, the transition form factor $F_{3\pi}$ is obtained close to the experimental data on account of current mass of quark.