Implications of a Light "Dark Higgs" Solution to the $g_{\mu }-2$ Discrepancy

Abstract

A light scalar $\varphi$ with mass $\lesssim 1$ GeV and muonic coupling $\mathcal{O}(10^{-3})$ would explain the 3.5 $\sigma$ discrepancy between the Standard Model (SM) muon $g-2$ prediction and experiment. Such a scalar can be associated with a light remnant of the Higgs mechanism in the "dark" sector. We suggest $\varphi \to l^{+}{l}^{-}$ bump hunting in $\mu \to e\nu \bar{\nu }\varphi$, ${\mu }^{-}p\to {\nu }_{\mu }n\varphi$ (muon capture), and $K^{\pm }\to {\mu }^{\pm }\nu \varphi$ decays as direct probes of this scenario. In a general setup, a potentially observable muon electric dipole moment $\lesssim 10^{-23}e\cdot \text{cm}$ and lepton flavor violating decays $\tau \to \mu (e)\varphi$ or $\mu \to e\varphi$ can also arise. Depending on parameters, a deviation in BR($H\to {\mu }^{+}{\mu }^{-}$) from SM expectations, due to Higgs coupling misalignment, can result. We illustrate how the requisite interactions can be mediated by weak scale vector-like leptons that typically lie within the reach of future LHC measurements.

Comments: 8 pages, 4 figures, references added, discussion on bounds from the charged Kaon decay extended