Exploring fake solutions in the sterile neutrino sector at long-baseline experiments

Active-sterile neutrino mixing is known to affect the neutrino oscillation probabilities at both short as well as long-baselines. In particular, constraints on active-sterile neutrino oscillation parameters can be obtained from long-baseline experiments such as T2HK and DUNE. We present here existence of fake solution in the appearance channel for the 3+1 scenario at long-baseline experiments. We show that the appearance probability is same for values of $\Delta m_{41}^2$ for which the fast oscillations are averaged out and for $\Delta m_{41}^2=(1/2)\Delta m_{31}^2$. The fake solution does not appear for the disappearance channel.