Secret Interactions of Sterile Neutrinos and MeV-scale gauge boson

Recent results from neutrino experiments show evidence for light sterile neutrinos which do not have any Standard Model interactions. These light sterile states are disfavored by cosmology due to the constraints from the Big Bang Nucleosynthesis and Large Scale Structure Formation. This tension could be solved if the sterile neutrino states had Secret Interaction with a light gauge boson $X$ with mass $M_X$ and coupling $g_X$, and with a field strength at least $10^3-10^4$ times larger than the Fermi constant. We show that such large interaction strength is ruled out due to the constraints from MINOS experiment. By performing an analysis on the Secret Interaction of the sterile neutrinos using the MINOS data and comparing with the results of cosmology, the CCFR experiment and the $(g-2)_\mu$ data we have found a concordance region for $g_X\sim (4-8)\times 10^{-4}$ and $M_X\sim (10-24)$~MeV.