Discovering true muonium at LHCb

We study the potential of the LHCb experiment to discover, for the first time, the μ⁺μ^- true muonium bound state. We propose a search for the vector 1³S₁ state, TM , which kinetically mixes with the photon and dominantly decays to e⁺e^- . We demonstrate that a search for η →γ TM , TM →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 η mass.