Discovering True Muonium at LHCb

Abstract

We study the potential of the LHCb experiment to discover, for the first time, the ${\mu }^{+}{\mu }^{-}$ true muonium bound state. We propose a search for the vector $1^3{S}_1$ state, $\mathcal{T}\mathcal{M}$, which kinetically mixes with the photon and dominantly decays to $e^{+}{e}^{-}$. We demonstrate that a search for $\eta \to \gamma \mathcal{T}\mathcal{M}$, $\mathcal{T}\mathcal{M}\to e^{+}{e}^{-}$ in a displaced vertex can exceed a significance of 5 standard deviations assuming statistical uncertainties. We present two possible searches: an inclusive search for the $e^{+}{e}^{-}$ vertex, and an exclusive search which requires an additional photon and a reconstruction of the $\eta$ mass.

12 pages, 5 figures; v2: edits from comments and review, matched to PRD version