A first prediction of the electromagnetic rare decays \$\eta^\prime\to\pi^0\gamma\gamma\$ and \$\eta^\prime\to\eta\gamma\gamma\$
(Jul 23, 2012)Abstract
The branching ratio of the electromagnetic rare decays
\$\eta\to\pi^0\gamma\gamma\$ and \$\eta^\prime(\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(\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.