Abstract
We investigate rare decays of tau leptons that occur via exchange of heavy on-shell neutrinos Nj (j = 1, 2). These neutrinos can be either Dirac or Majorana, and are considered to be almost degenerate in mass. The decays can thus be either lepton number conserving (LNC), τ∓ → π∓Nj → π∓μ∓π±, or lepton number violating (LNV), τ∓ → π∓Nj → π∓μ±π∓. If neutrinos are Dirac, only LNC decays are possible. If they are Majorana, both LNC and LNV are possible. We derive the corresponding expressions for the effective decay widths \( {\Gamma}_{\textrm{eff},\mp}^{\left(\textrm{X}\right)} \) (X=LNC, LNV) of these rare decays, where we account for N1-N2 overlap and oscillation effects and for the finite detector length effects. We then numerically evaluate these decay widths as well as the related CP violation asymmetry width \( \Delta {\Gamma}_{\textrm{CP}}^{\left(\textrm{X}\right)}=\left({\Gamma}_{\textrm{eff},-}^{\left(\textrm{X}\right)}-{\Gamma}_{\textrm{eff},+}^{\left(\textrm{X}\right)}\right) \). We conclude that for certain, presently allowed, ranges of the heavy-light neutrino mixing parameters, such decays and asymmetries could be observed in Belle II experiment.
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Acknowledgments
This work of G.C.was supported in part by FONDECYT (Chile) Grant No. 1220095, The work of C.S.K. was supported by NRF of Korea (NRF-2022R1A5A1030700 and NRF-2022R1I1A1A01055643).
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Cvetič, G., Kim, C.S. Rare tau decays via exchange of on-shell almost degenerate Majorana neutrinos, τ∓ → π∓Nj → π∓μ∓π± and τ∓ → π∓Nj → π∓μ±π∓. J. High Energ. Phys. 2024, 215 (2024). https://doi.org/10.1007/JHEP02(2024)215
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DOI: https://doi.org/10.1007/JHEP02(2024)215