Analysis of the $e^{+}e^{-}\rightarrow\pi^{0}\gamma$ process using anomaly sum rules approach

TL;DR

This paper applies the Anomaly Sum Rules approach to analyze the $e^{+}e^{-} ightarrow ext{pi}^0 ext{gamma}$ process, successfully describing experimental data and proposing a method for pole region analysis.

Contribution

It introduces a modified ASR approach for better description of the process near the pole, providing new restrictions on model parameters.

Findings

Good description of data far from the pole

Proposed method for pole region analysis

Restrictions on parameters of the modified ASR approach

Abstract

The process $e^{+}e^{-}\rightarrow\gamma^{*}\rightarrow \pi^{0}\gamma$ was considered using time-like pion transition form factor, obtained in the approach of the Anomaly Sum Rules(ASR). The total cross section and angular distribution of the process was calculated. As the result of the comparison with the data it was shown that ASR approach provides their good description in the regions far from the pole. Also there was proposed a method allowing to give reasonable description of data in the region of pole within the ASR approach. The strong restrictions for the parameters of the modified ASR approach were obtained.