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

Electroweak Corrections to the True Muonium Hyperfine Splitting