Discovery potential of T2K and NO v A in the presence of a light sterile neutrino

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 nova 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 v μ → v e and $$ {overline{v}}_{mu}to {overline{v}}_e $$ 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 $$ delta $$ 13 = $$ delta $$ and the neutrino mass hierarchy get substantially deteriorated. the exact loss of sensitivity depends on the value of the unknown cp-phase $$ delta $$ 14. finally, we estimate the discovery potential of total cp-violation (i.e., induced simultaneously by the two cp-phases $$ delta $$ 13 and $$ delta $$ 14), and the capability of the two experiments of reconstructing the true values of such cp-phases. the typical (1 $$ sigma $$ level) uncertainties on the reconstructed phases are approximately 400 for $$ delta $$ 13 and 500 for $$ delta $$ 14.