Hyperfine Splitting in True Muonium to $\mathcal{O}(m_{\mu }{\alpha }^6)$: Two Photon Annihilation Contribution from Other Flavors

Abstract

The two-photon-annihilation contribution to the true muonium hyperfine splitting arising from $e$ and $\tau$ loops is obtained analytically at order $m_{\mu }{\alpha }^6$. The contribution to the hyperfine splitting is $-2.031092873m_{\mu }{\alpha }^6/n^3{\pi }^2=-793.926988/n^3$ MHz. The contribution to the triplet true muonium decay rate has also been obtained and was found to be $9.825708266m_{\mu }{\alpha }^6/n^3{\pi }^2=3840.737698/n^3$ MHz. Additional results have been computed for other purely leptonic bound states.

4 pages, 1 Figure, Updated to match journal version

References in corpus (6)

• Test of lepton universality using $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• Muonic hydrogen and MeV forces
• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• Positronium energy levels at order $m{\alpha }^7$: light-by-light scattering in the two-photon-annihilation channel
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
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Cited by in corpus (3)

• Hadronic Vacuum Polarization in True Muonium
• Applying Bayesian Inference to Galileon Solutions of the Muon Problem
• Decay of the dimuonium into a photon and a neutral pion