True muonium resonant production at $e^+e^-$ colliders with standard crossing angle

Abstract

True muonium ($\mu^+\mu^-$) is the heaviest and smallest bound state not involving quantum chromodynamics, after true tauonium ($\tau^+\tau^-$) and mu-tauonium ($\mu^\pm\tau^\mp$). Unlike atoms containing $\tau$ particles, the muon lifetime is long enough to allow observation of true muonium (TM) decays and transitions. One of the proposed methods to observe the spin 1 fundamental state of TM, which has the smallest lifetime among TM spin 1 states, was to build an $e^+e^-$ collider with a large crossing angle ($\theta \sim 30^\circ$) in order to provide TM with a large boost and detect its decay vertex in $e^+ e^-$. The following paper will instead show that TM excited states ($n\geq2$) can be observed in relatively large quantities ($\mathcal{O}$(10)/month) at a feasible $e^+e^-$ collider with standard crossing angles, after setting their center-of-mass energy to the TM mass ($\sim2m_{\mu}=211.4$ MeV).