Implications of a light “dark Higgs” solution to the $g_{\mu }-2$ discrepancy

A light scalar $\varphi$ with mass $\lesssim 1\mathrm{GeV}$ 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 $\mu \to e\nu \overline{\nu }\varphi$, ${\mu }^{-}p\to {\nu }_{\mu }n\varphi$ (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 $\lesssim {10}^{-23}e\mathrm{cm}$ 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.

Figure 1

One-loop $\varphi$ contribution to lepton dipole moments.

Figure 2

Central values and one-sigma band of ${\lambda }_S^{\mu }$, required by the measured value of $\mathrm{\Delta }{a}_{\mu }$ in Eq. (1).

Figure 3

Muon electric dipole moment, for various $CP$-violating phases, assuming that $\mathrm{\Delta }{a}_{\mu }$ agrees with the measured value of $g_{\mu }-2$ within one sigma.

Figure 4

Branching ratios of $\mu \to e\nu \overline{\nu }\varphi$ and $K^{+}\to {\mu }^{+}\nu \varphi$, assuming that $\mathrm{\Delta }{a}_{\mu }$ agrees with the measured value of $g_{\mu }-2$ within one sigma.