Probing Neutrinophilic Scalars in Muon Decays

RESUMO

The non-standard self-interactions of neutrinos could be induced by (light) scalars that couple primarily to neutrinos. In this work, we investigate the effects of neutrinophilic scalars $\phi$ on muon decays at the tree, 1-loop and 2-loop levels, considering both Dirac and Majorana neutrinos. The most phenomenologically interesting processes are the 1-loop corrections of $\phi$ to the SM muon decay and the four-body muon decays $\mu^- \to e^- \nu_\mu \nu_\mu \phi,\, e^- \bar\nu_e \bar\nu_e \phi$, both induced by the coupling $h_{e\mu}$ of $\phi$ to Majorana neutrinos. The infrared divergences in these processes cancel with each other, yielding an infrared-safe inclusive decay width. The precise $G_F$ measurements constrain the coupling $|h_{e\mu}|$ down to roughly $0.027$, with the scalar mass $m_\phi$ constrained up to roughly $5.9$ TeV. For $m_\phi \gtrsim {\cal O}({\rm GeV})$, the $G_F$ measurements are more stringent than other existing laboratory, astrophysical and cosmological constraints. Some other $\phi$-induced processes are also possible, which are, however, heavily suppressed by the small couplings, tiny neutrino masses and/or the loop factor.