Signals of eV-scale sterile neutrino at long baseline neutrino experiments

While most of the results of the neutrino oscillation experiments can be accommodated within the standard paradigm of three active flavor, there are tantalizing hints of an light eV-scale sterile neutrino from anomalous results of a few short baseline experiments. This additional light sterile neutrino is expected to leave an imprint on the physics observables pertaining to standard unknowns such as determination of the Dirac-type leptonic $CP$ phase, $\delta_{13}$, the question of neutrino mass hierarchy and the octant of $\theta_{23}$. The upcoming long baseline neutrino experiments such as T2HK, DUNE and P2O will be sensitive to active - sterile mixing. In the present work, we examine and assess the capability of these long baseline experiments to probe the sterile neutrino at the level of probabilities and event rates. We perform a detailed study by taking into account the values of parameters that are presently allowed and (a) study the impact on $CP$ violation by examining the role played by various appearance and disappearance channels, (b) address the question of disentangling the intrinsic effects from extrinsic effects in the standard paradigm as well as three active plus one light sterile neutrino, and finally (c) assess the ability of these long baseline experiments to distinguish between the two scenarios. Our results indicate that for the true values of sterile parameters and for all values of $\delta_{13}$, the sensitivity of P2O is the lowest while the sensitivity of T2HK is modest ($<3\,\sigma$) and the sensitivity of DUNE is $> 3\,\sigma$. For larger values of the sterile mixing angles, there is an improvement in the sensitivity for all the three considered experiments.