Neutrino properties from muonium-antimuonium mixing

The nature of neutrino mass -- whether neutrinos are Dirac or Majorana particles -- remains one of the central open questions in particle physics. While observation of neutrinoless double beta decay would confirm the Majorana case, the absence of a signal offers no definitive insight. In light of this, we investigate muonium-antimuonium mixing -- proposed for further study at the MACE experiment -- as an alternative probe of neutrino properties. We compute the mixing amplitude in the Standard Model minimally extended to include massive Dirac or Majorana neutrinos, and correct previous calculations by properly treating the relevant infrared scales. As the GIM mechanism strongly suppresses the Dirac contribution, we explore whether relaxing unitarity of the PMNS matrix can enhance the mixing without obscuring neutrino properties. Surprisingly, the answer to this question is negative. We also examine the pseudo-Dirac case -- predominantly Dirac neutrinos with small Majorana masses -- and find that this scenario can significantly enhance the mixing compared to the pure Dirac case, especially for normal mass ordering.