A first prediction of the electromagnetic rare decays $\eta^\prime\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$

TL;DR

This paper predicts the branching ratios of rare electromagnetic decays of eta prime mesons using theoretical models, providing first estimates to guide future experimental measurements.

Contribution

It offers the first theoretical predictions for the unmeasured $ ext{eta}^ ext{prime} o ( ext{pi}^0, ext{eta}) ext{gamma} ext{gamma}$ decays, validating the approach with known decay data.

Findings

Predicted branching ratios for $ ext{eta}^ ext{prime} o ( ext{pi}^0, ext{eta}) ext{gamma} ext{gamma}$.

Validation of the theoretical framework with existing $ ext{eta} o ext{pi}^0 ext{gamma} ext{gamma}$ data.

Guidance for upcoming experiments like KLOE-2 and BES-III.

Abstract

The branching ratio of the electromagnetic rare decays $\eta\to\pi^0\gamma\gamma$ and $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ are analysed in terms of scalar and vector meson exchange contributions using the frameworks of the Linear Sigma Model and Vector Meson Dominance, respectively. The measured $\eta\to\pi^0\gamma\gamma$ process serves as a test of our approach while the non yet measured $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ reactions are predicted for the first time. Our prediction for the $\eta\to\pi^0\gamma\gamma$ decay agrees with recent experimental reported values, thus supporting the validity of our framework. Therefore, our predictions for the $\eta^\prime\to\pi^0\gamma\gamma$ and $\eta^\prime\to\eta\gamma\gamma$ decays should be taken as a first indication of the possible values of the associated branching ratios. We hope these predictions to be interesting and useful for experiments such as KLOE-2, Crystal Ball, WASA, and BES-III where these processes are expected to be measured in the next future.