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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$σ$ if the three new mixing angles ($θ_{14}, θ_{24}, θ_{34}$) are all close to $θ_{13}$. In contrast, it can decrease to 4$σ$ if the least constrained mixing angle $θ_{34}$ is close to its upper limit $\sim 30^0$. We also assess the sensitivity to the CPV induced both by the standard CP-phase $δ_{13} \equiv δ$, and the new CP-phases $δ_{14}$ and $δ_{34}$. In the 3+1 scheme, the discovery potential of CPV induced by $δ_{13}$ gets deteriorated compared to the 3$ν$ case. In particular, the maximal sensitivity (reached around $δ_{13}$ $\sim$ $\pm$ $90^0$) decreases from $5σ$ to $4σ$ if all the three new mixing angles are close to $θ_{13}$. It can further diminish to almost $3σ$ if $θ_{34}$ is large ($\sim 30^0$). The sensitivity to the CPV due to $δ_{14}$ can reach 3$σ$ for an appreciable fraction of its true values. Interestingly, $θ_{34}$ and its associated phase $δ_{34}$ can influence both the $ν_e$ appearance and $ν_μ$ disappearance channels via matter effects, which in DUNE are pronounced. Hence, DUNE can also probe CPV induced by $δ_{34}$ provided $θ_{34}$ is large. We also reconstruct the two phases $δ_{13}$ and $δ_{14}$. The typical 1$σ$ uncertainty on $δ_{13}$ ($δ_{14}$) is $\sim20^0$ ($30^0$) if $θ_{34} =0$. The reconstruction of $δ_{14}$ (but not that of $δ_{13}$) degrades if $θ_{34}$ is large.