Implications of δ_CP = −90^∘ towards determining hierarchy and octant at T2K and T2K-II

The T2K experiment has provided the first hint for the best-fit value for the leptonic CP phase δ_CP ∼− 90^∘ from neutrino data. This is now corroborated by the NOνA neutrino runs. We study the implications for neutrino mass hierarchy and octant of θ₂₃ in the context of this data assuming that the true value of δ_CP in nature is − 90^∘ . Based on simple arguments on degeneracies in the probabilities, we show that a clear signal of δ_CP = −90^∘ coming from T2K neutrino (antineutrino) data is only possible if the true hierarchy is normal and the true octant is higher (lower). Thus, if the T2K neutrino and antineutrino data are fitted separately and both give the true value of δ_CP = −90∘, this will imply that nature has chosen the true hierarchy to be normal and δ23 ≈ 45∘. However, we find that the combined fit of neutrino and antineutrino data will still point to true hierarchy as normal but the octant of θ₂₃ will remain undetermined. We do our analysis for both, the current projected exposure (7.8 × 1021 pot) and planned extended exposure (20 × 1021 pot). We also present the CP discovery potential of T2K emphasizing on the role of antineutrinos. We find that one of the main contributions of the antineutrino data is to remove the degenerate solutions with the wrong octant. Thus, the antineutrino run plays a more significant role for those hierarchy-octant combinations for which this degeneracy is present. If this degeneracy is absent, then only neutrino run gives a better result for fixed θ₁₃. However, if we marginalize over θ₁₃ then, sensitivity corresponding to mixed run can be better than pure neutrino run