Electroweak corrections to the true muonium hyperfine splitting

In contrast to other atomic systems, in true muonium (${\mu }^{+}{\mu }^{-}$) the leading-order $Z$ boson corrections to the hyperfine splitting are shown to be experimentally accessible in the near future. This contribution ($-109\mathrm{MHz}$) constitutes a necessary contribution to a full $\mathcal{O}(m{\alpha }^7)$ calculation of the true muonium hyperfine splitting. This calculation would enable a number of possible solutions to the muon problem to be constrained. Additionally, we compute the general expression for a pseudovector coupling to particle-antiparticle bound states at leading order, including the annihilation channel.