Joint short- and long-baseline constraints on light sterile neutrinos

Recent studies provide evidence that long-baseline (LBL) experiments are sensitive to the extra $CP$ phases involved with light sterile neutrinos, whose existence is suggested by several anomalous short-baseline (SBL) results. We show that, within the $3+1$ scheme, the combination of the existing SBL data with the LBL results coming from the two currently running experiments, NOνA and T2K, enables us to simultaneously constrain two active-sterile mixing angles, θ₁₄ and θ₂₄, and two $CP$ phases, δ₁₃≡δ and δ₁₄, although the information on the second $CP$ phase is still weak. The two mixing angles are basically determined by the SBL data, while the two $CP$ phases are constrained by the LBL experiments, once the information coming from the SBL setups is taken into account. We also assess the robustness or fragility of the estimates of the standard 3-flavor parameters in the more general $3+1$ scheme. To this regard we find that (i) the indication of $CP$ violation found in the 3-flavor analyses persists also in the $3+1$ scheme, with δ₁₃≡δ having still its best-fit value around -π/2, (ii) the 3-flavor weak hint in favor of the normal hierarchy becomes even less significant when sterile neutrinos come into play, (iii) the weak indication of nonmaximal θ₂₃ (driven by NOνA disappearance data) persists in the $3+1$ scheme, where maximal mixing is disfavored at almost the 90% C.L. in both normal and inverted mass hierarchy, and (iv) the preference in favor of one of the two octants of θ₂₃ found in the 3-flavor framework (higher octant for inverted mass hierarchy) is completely washed out in the $3+1$ scheme.