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 5σ if the three new mixing angles (θ14, θ24, θ34) are all close to θ13. In contrast, it can decrease to 4σ if the least constrained mixing angle θ34 is close to its upper limit ∼ 300. We also assess the sensitivity to the CPV induced both by the standard CP-phase δ13 ≡ δ, and the new CP-phases δ14 and δ34. In the 3+1 scheme, the discovery potential of CPV induced by δ13 gets deteriorated compared to the 3ν case. In particular, the maximal sensitivity (reached around δ13 ∼ ± 900) decreases from 5σ to 4σ if all the three new mixing angles are close to θ13. It can further diminish to almost 3σ if θ34 is large (∼ 300). The sensitivity to the CPV due to δ14 can reach 3σ for an appreciable fraction of its true values. Interestingly, θ34 and its associated phase δ34 can influence both the νe appearance and νμ disappearance channels via matter effects, which in DUNE are pronounced. Hence, DUNE can also probe CPV induced by δ34 provided θ34 is large. We also reconstruct the two phases δ13 and δ14. The typical 1σ uncertainty on δ13 (δ14) is ∼ 200 (300) if θ34 = 0. The reconstruction of δ14 (but not that of δ13) degrades if θ34 is large.