Hidden Interactions of Sterile Neutrinos As a Probe For New Physics

Recent results from neutrino experiments show evidence for light sterile neutrinos which do not have any Standard Model interactions. In this work we study the hidden interaction of sterile neutrinos with an "MeV scale" gauge boson (the $\nu_s$HI model) with mass $M_X$ and leptonic coupling $g^\prime_l$. By performing an analysis on the $\nu_s$HI model using the data of the MINOS neutrino experiment we find that the values above $G_X/G_F=92.4$ are excluded by more than $2\sigma$ C.L., where $G_F$ is the Fermi constant and $G_X$ is the field strength of the $\nu_s$HI model. Using this model we can also probe other new physics scenarios. We find that the region allowed by the $(g-2)_\mu$ discrepancy is entirely ruled out for $M_X\lesssim 100$ MeV. Finally, the secret interaction of sterile neutrinos has been to solve a conflict between the sterile neutrinos and cosmology. It is shown here that such an interaction is excluded by MINOS for $g^\prime_s> 1.6\times10^{-2}$. This exclusion, however, does depend on the value of $g_l^{\prime}$.