Probing Neutrinophilic Scalars in Muon Decays

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 $\mathrm{\mid }{h}_{e\mu }\mathrm{\mid }$ down to roughly $0.027$, with the scalar mass $m_{\phi }$ constrained up to roughly $5.9$ TeV. For $m_{\phi }\gtrsim \mathcal{O}(\mathrm{G}\mathrm{e}\mathrm{V})$, 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.