Assessment of the $a_2(1320)$ tensor-meson contribution to $\eta /{\eta }^{\prime }\to {\pi }^0\gamma \gamma$ decays

Abstract

In light of the recent measurement of the $\eta \to {\pi }^0\gamma \gamma$ decay by the KLOE-2 Collaboration, a previous analysis including vector- and scalar-meson exchange contributions using the VMD and L$\sigma$M frameworks, respectively, is extended in the present study to incorporate the effects of the $a_2(1320)$ tensor meson within a chiral context. Although the individual contribution of the $a_2$ is negligible, its destructive interference with the vector-meson resonances is found to be significant, representing approximately $18\%$ of the total signal and substantially affecting the diphoton invariant-mass distribution, especially at low $m_{\gamma \gamma }^2$ values. The total decay rate is calculated to be $\Gamma (\eta \to {\pi }^0\gamma \gamma )=0.154(22)$ eV, which corresponds to a branching ratio of $\mathrm{BR}(\eta \to {\pi }^0\gamma \gamma )=1.17(17)\times 10^{-4}$. This result is approximately $5\sigma$ below the reported value of the PDG, $2.55(22)\times 10^{-4}$, while it is in very good agreement with the KLOE-2 measurement, $0.98(11_{\mathrm{stat}})(14_{\mathrm{syst}})\times 10^{-4}$. In contrast, the total contribution of the $a_2$ is found to be negligible in ${\eta }^{\prime }\to {\pi }^0\gamma \gamma$, as this process is completely dominated by the exchange of an on-shell $\omega$ vector resonance.

Comments: 9 pages, 6 figures, 2 tables