Scouring meson decays for true muonium

Rare meson decay experiments promise to measure branching ratios as small as ${10}^{-13}$. This presents an opportunity to discover the ${\mu }^{+}{\mu }^{-}$ bound state true muonium. We consider a set of possible channels, all with branching ratios above $\sim {10}^{-11}$. For the electromagnetic decays $\eta /{\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma$, theoretical and phenomenological form factors $F_{\eta /{\eta }^{\prime }\gamma {\gamma }^{*}}(Q^2)$ allow predictions of $\mathcal{BR}({\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma )\sim 4.8\times {10}^{-10}$ and $\mathcal{BR}({\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma )\sim 3.7\times {10}^{-11}$ at the 5% level. Discussion of experimental prospects and potential backgrounds are made.

Figure 1

One of the Feynman diagrams of $\eta /{\eta }^{\prime }\to {\gamma }^{*}{\gamma }^{*}\to ({\mu }^{+}{\mu }^{-})\gamma$ which contribute to the branching ratio at $\mathcal{O}({\alpha }^5)$ and is proportional to $F_{{\gamma }^{*}{\gamma }^{*}}(z_1,z_2)$.