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

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.