Abstract:We study the impact of one light sterile neutrino on the prospective data expected to come from the two presently running long-baseline experiments T2K and NOνA when they will accumulate their full planned exposure. Introducing for the first time, the bi-probability representation in the 4-flavor framework, commonly used in the 3-flavor scenario, we present a detailed discussion of the behavior of the ν µ → ν e andν µ →ν e transition probabilities in the 3+1 scheme. We also perform a detailed sensitivity study of these two experiments (both in the stand-alone and combined modes) to assess their discovery reach in the presence of a light sterile neutrino. For realistic benchmark values of the mass-mixing parameters (as inferred from the existing global short-baseline fits), we find that the performance of both these experiments in claiming the discovery of the CP-violation induced by the standard CP-phase δ 13 ≡ δ, and the neutrino mass hierarchy get substantially deteriorated. The exact loss of sensitivity depends on the value of the unknown CP-phase δ 14 . Finally, we estimate the discovery potential of total CP-violation (i.e., induced simultaneously by the two CP-phases δ 13 and δ 14 ), and the capability of the two experiments of reconstructing the true values of such CP-phases. The typical (1σ level) uncertainties on the reconstructed phases are approximately 40 0 for δ 13 and 50 0 for δ 14 .