Two-Higgs doublet solution to the LSND, MiniBooNE and muon $g-2$ anomalies

We show that one of the simplest extensions of the Standard Model, the addition of a second Higgs doublet, when combined with a dark sector singlet scalar, allows us to $i)$ explain the long-standing anomalies in the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE (MB) while maintaining compatibility with the null result from KARMEN, $ii)$ obtain, in the process, a portal to the dark sector, and $iii)$ comfortably account for the observed value of the muon $g-2$. Three singlet neutrinos allow for an understanding of observed neutrino mass-squared differences via a Type I seesaw, with two of the lighter states participating in the interaction in both LSND and MB. We obtain very good fits to energy and angular distributions in both experiments. We explain features of the solution presented here and discuss the constraints that our model must satisfy. We also mention prospects for future tests of its particle content.

Figure 1

Feynman diagram of the scattering process in our model which leads to the excess at LSND and MB.

Figure 2

Top panels: The MB electronlike events (backgrounds and signal) from Ref. [20], versus the visible energy ${\mathrm{E}}_{\mathrm{vis}}$ (left panel) and versus the cosine of the emitted angle of the light (right panel), for neutrino runs. The blue solid line is the prediction of our model. Bottom panels: The energy distribution (left panel) of the LSND data [19] for $R_{\gamma }>10$, and the angular distribution (right panel) of the light due to the electronlike final state, for $R_{\gamma }>1$. The shaded blue region in both panels is our fit, and other shaded regions are the backgrounds.