Chiral anomaly transition form factor of γ → 3π in nonlocal quark model

Alexey Zhevlakov

doi:10.1051/epjconf/201920402001

Abstract

Chiral anomaly of gamma transition into three pions are studied in a framework of nonlocal chiral quark model. In the local limit the result is in agreement with chiral perturbative theory and reproducesWess-Zumino-Witten anomaly. Transition form factor of gamma into three pions in nonlocal quark model has a correction which vanishes in local limit.

Highlights

Chiral anomaly of gamma transition into three pions are studied in a framework of nonlocal chiral quark model
Chiral anomaly plays an important role in description of many processes of particle physics, in particular, which are connected with pseudoscalar mesons and their interaction with external vector or axial-vector fields
Transition γ∗ → 3π form factor plays an important role in understanding of chiral anomaly and pseudoscalar meson properties

Summary

Introduction

Chiral anomaly plays an important role in description of many processes of particle physics, in particular, which are connected with pseudoscalar mesons and their interaction with external vector or axial-vector fields. One of known process which goes through anomaly is decay of neutral pseudoscalar meson into pair of photons. This process gives main mode of decay and has branching ∼ 98.823 % [1]. Kazuo Fujikawa [3] has shown that the imaginary part of effective action which describes a chiral anomaly goes from Jacobian of productive functional. After integration by quark fields we obtain amplitudes which describe chiral anomalies. Well-known chiral anomaly of pion decay into pair of photons has the following form: A(π0 → γγ) = Fγγ(Mπ20 ) μναβ μk1ν αk2β,. The process of γπ− → π−π0 has a connection to the WZW anomalous effective action and amplitude of reaction has a form. New experimental data of Primakoff reaction πγ → ππ can be extracted from the data which obtained at CERN COMPASS experiment and may be measured on upgraded version of the experiment facility

Nonlocal model

Nonlocal quark model

Transition form factor

Conclusion