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

TL;DR

This paper proposes a method to observe excited states of true muonium at standard $e^+e^-$ colliders by tuning the center-of-mass energy to the TM mass, enabling feasible detection without large crossing angles.

Contribution

It demonstrates that true muonium excited states can be produced and observed in significant quantities at standard colliders by adjusting the energy, challenging previous requirements for large crossing angles.

Findings

True muonium excited states can be observed at feasible collider settings.

Production rates of about 10 per month for excited states are achievable.

Standard crossing angles suffice for detection, simplifying experimental setup.

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).