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

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.

Comments: 6 pages, uses PoS style. Talk presented at the 6th International Conference on Quarks and Nuclear Physics (QNP2012), École Polytechnique (Palaiseau), France, April 16-20, 2012