Parameter degeneracy and hierarchy sensitivity of NO$ u$A in presence of sterile neutrino

The first hint of neutrino mass hierarchy is expected to come from the NO$ u$A experiment in Fermilab as the present best-fit parameter space i.e., normal hierarchy and $delta_{CP}=-90^circ$ is the favourable parameter space for NO$ u$A where there is no degeneracy. But this situation may change if the standard three flavour framework is not complete and there is existence of new physics. In this work we consider the presence of an extra light sterile neutrino at the eV scale and study the new degeneracies which are absent in the standard three flavour framework. We also study the effect of these new degeneracies on the hierarchy measurement of NO$ u$A.