Probing Neutrinophilic Scalars in Muon Decays

Abstract

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 $ϕ$ 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 $ϕ$ to the SM muon decay and the four-body muon decays $μ^- \to e^- ν_μν_μϕ,\, e^- \barν_e \barν_e ϕ$, both induced by the coupling $h_{eμ}$ of $ϕ$ 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 $|h_{eμ}|$ down to roughly $0.027$, with the scalar mass $m_ϕ$ constrained up to roughly $5.9$ TeV. For $m_ϕ\gtrsim {\cal O}({\rm GeV})$, the $G_F$ measurements are more stringent than other existing laboratory, astrophysical and cosmological constraints. Some other $ϕ$-induced processes are also possible, which are, however, heavily suppressed by the small couplings, tiny neutrino masses and/or the loop factor.