Interpreting NO$\nu$A and T2K data in the presence of a light sterile neutrino

We study in detail the impact of a light sterile neutrino in the interpretation of the latest data of the long baseline experiments NO$\nu$A and T2K, assessing the robustness/fragility of the estimates of the standard 3-flavor parameters with respect to the perturbations induced in the 3+1 scheme. We find that the 3-flavor ($\sim$2.4$\sigma$) indication in favor of the normal ordering remains almost unaltered in the 4-flavor scheme ($\sim$2.2$\sigma$). We also show that, in the (preferred) normal neutrino ordering, the indication in favor of CP-violation found in the 3-flavor framework ($\sim$2.0$\sigma$) appreciably decreases in the 3+1 scheme ($\sim$1.2$\sigma$). Regarding the atmospheric mixing angle $\theta_{23}$, the preference for the higher octant of $\theta_{23}$ shows a sensible reduction in the presence of a sterile neutrino ($\sim$1.7$\sigma$ vs $\sim$1.0$\sigma$). Our analysis also demonstrates that it is possible to attain constraints on the new CP-phase $\delta_{14}$, which interestingly has best fit value close to that of the standard CP phase $\delta_{13}$. Finally, we highlight a striking positive correlation among the standard CP-phase $\delta_{13}$ and the new CP-phase $\delta_{14}$.