Scouring meson decays for true muonium

Abstract

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 $\sim10^{-11}$. For the electromagnetic decays $\eta/\eta'\rightarrow(\mu^+\mu^-)\gamma$, theoretical and phenomenological form factors $F_{\eta/\eta'\gamma\gamma^*}(Q^2)$ allow predictions of $\mathcal{BR}(\eta'\rightarrow (\mu^+\mu^-) \gamma)\sim 4.8\times10^{-10}$ and $\mathcal{BR}(\eta'\rightarrow (\mu^+\mu^-) \gamma)\sim 3.7\times10^{-11}$ at the 5% level. Discussion of experimental prospects and potential backgrounds are made.