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 $\sim 10^{-11}$. For the electromagnetic decays $\eta /{\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma$, theoretical and phenomenological form factors $F_{\eta /{\eta }^{\prime }\gamma {\gamma }^{\ast }}(Q^2)$ allow predictions of $\mathcal{B}\mathcal{R}({\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma )\sim 4.8\times 10^{-10}$ and $\mathcal{B}\mathcal{R}({\eta }^{\prime }\to ({\mu }^{+}{\mu }^{-})\gamma )\sim 3.7\times 10^{-11}$ at the 5% level. Discussion of experimental prospects and potential backgrounds are made.

5 pages, 1 figure

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