Physics Reach of DUNE with a Light Sterile Neutrino

We investigate the implications of one light eV scale sterile neutrino on the physics potential of the proposed long-baseline experiment DUNE. If the future short-baseline experiments confirm the existence of sterile neutrinos, then it can affect the mass hierarchy (MH) and CP-violation (CPV) searches at DUNE. The MH sensitivity still remains above 5$\sigma$ if the three new mixing angles (${\theta }_{14},{\theta }_{24},{\theta }_{34}$) are all close to ${\theta }_{13}$. In contrast, it can decrease to 4$\sigma$ if the least constrained mixing angle ${\theta }_{34}$ is close to its upper limit $\sim {30}^0$. We also assess the sensitivity to the CPV induced both by the standard CP-phase $\delta_{13} \equiv \delta$,andthenewCP-phases$\delta_{14}$and$\delta_{34}$. In the 3+1 scheme, the discovery potential of CPV induced by ${\delta }_{13}$ gets deteriorated compared to the 3$\nu$ case. In particular, the maximal sensitivity (reached around ${\delta }_{13}$ $\sim$ $\pm$ ${90}^0$) decreases from $5\sigma$ to $4\sigma$ if all the three new mixing angles are close to ${\theta }_{13}$. It can further diminish to almost $3\sigma$ if ${\theta }_{34}$ is large ($\sim {30}^0$). The sensitivity to the CPV due to ${\delta }_{14}$ can reach 3$\sigma$ for an appreciable fraction of its true values. Interestingly, ${\theta }_{34}$ and its associated phase ${\delta }_{34}$ can influence both the ${\nu }_e$ appearance and ${\nu }_{\mu }$ disappearance channels via matter effects, which in DUNE are pronounced. Hence, DUNE can also probe CPV induced by ${\delta }_{34}$ provided ${\theta }_{34}$ is large. We also reconstruct the two phases ${\delta }_{13}$ and ${\delta }_{14}$. The typical 1$\sigma$ uncertainty on ${\delta }_{13}$ (${\delta }_{14}$) is $\sim {20}^0$ (${30}^0$) if ${\theta }_{34}=0$. The reconstruction of ${\delta }_{14}$ (but not that of ${\delta }_{13}$) degrades if ${\theta }_{34}$ is large.