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 $g_l^{\prime}$.
