Implications of a Light "Dark Higgs" Solution to the $g_μ-2$ Discrepancy

A light scalar $ϕ$ with mass $\lesssim 1$ GeV and muonic coupling $\mathcal{O}(10^{-3})$ would explain the 3.5 $σ$ 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 $ϕ\to l^+l^-$ bump hunting in $μ\to eν\barνϕ$, $μ^-p\toν_μnϕ$ (muon capture), and $K^\pm\to μ^\pmνϕ$ decays as direct probes of this scenario. In a general setup, a potentially observable muon electric dipole moment $\lesssim 10^{-23}\ e \cdot\textrm{cm}$ and lepton flavor violating decays $τ\toμ(e) ϕ$ or $μ\to e ϕ$ can also arise. Depending on parameters, a deviation in BR($H\toμ^+μ^-$) 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.

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