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 $\varphi$ 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 decay $\mu \to e\varphi \varphi$ and $\varphi$-induced decay $\mu \to e\gamma$ at the 2-loop order from the same coupling $g_{\mathrm{eff}}$, and the 1-loop corrections of $\varphi$ to the SM muon decay and the four-body muon decays ${\mu }^{-}\to e^{-}{\nu }_{\mu }{\nu }_{\mu }\varphi ,e^{-}{\bar{\nu }}_e{\bar{\nu }}_e\varphi$, both induced by the coupling $h_{e\mu }$ of $\varphi$ to Majorana neutrinos. The current experimental bounds on $\mu \to e\gamma$ provide the most stringent limits on the coupling $g_{\mathrm{eff}}$, up to roughly 0.064, for the scalar mass $m_{\varphi }\gtrsim 8.7$ MeV. The precise $G_F$ measurements constrain the coupling $|h_{e\mu }|$ down to roughly $0.027$, with the scalar mass $m_{\varphi }$ constrained up to roughly $5.9$ TeV. For $m_{\varphi }\gtrsim \mathcal{O}(\mathrm{GeV})$, the $G_F$ measurements are more stringent than other existing laboratory, astrophysical and cosmological constraints. Some other $\varphi$-induced processes are also possible, which are, however, heavily suppressed by the tiny neutrino masses and/or the loop factor.

arXiv comment17 pages, 10 figures; adding more channels induced by the neutrinophilic scalar, typos fixed