Study of parameter degeneracy and hierarchy sensitivity of NO$\nu$A in presence of sterile neutrino

The first hint of the neutrino mass hierarchy is believed to come from the long-baseline experiment NO$\nu$A. Recent results from the NO$\nu$A shows a mild preference towards the CP phase $\delta_{13} = -90^\circ$ and normal hierarchy. Fortunately this is the favorable area of the parameter space which does not suffer from the hierarchy-$\delta_{13}$ degeneracy and thus NO$\nu$A can have good hierarchy sensitivity for this true combination of hierarchy and $\delta_{13}$. Apart from the hierarchy-$\delta_{13}$ degeneracy there is also the octant-$\delta_{13}$ degeneracy. But this does not affect the favorable parameter space of NO$\nu$A as this degeneracy can be resolved with a balanced neutrino and antineutrino run. However, ff we consider the existence of a light sterile neutrino then there may be additional degeneracies which can spoil the hierarchy sensitivity of NO$\nu$A even in the favorable parameter space. In the present work we find that apart from the degeneracies mentioned above, there are additional hierarchy and octant degeneracies that appear with the new phase $\delta_{14}$ in the presence of a light sterile neutrino in the eV scale. In contrast to the hierarchy and octant degeneracies appearing with $\delta_{13}$, the parameter space for hierarchy-$\delta_{14}$ degeneracy is different in neutrinos and antineutrinos though the octant-$\delta_{14}$ degeneracy behaves similarly in neutrinos and antineutrinos. We study the effect of these degeneracies on the hierarchy sensitivity of NO$\nu$A for the true normal hierarchy.