Large-θ13 perturbation theory of neutrino oscillation for long-baseline experiments

The Cervera et al. formula, the best known approximate formula of neutrino oscillation probability for long-baseline experiments, can be regarded as a second-order perturbative formula with small expansion parameter ϵ ≡ ∆ m 21 2 ∆ m 31 2 ≃ 0 . 03 under the 21assumption s 13 ≃ ϵ. If θ 13 is large, as suggested by a candidate ν e event at T2K as well as the recent global analyses, higher order corrections of s 13 to the formula would be needed for better accuracy. We compute the corrections systematically by formulating a perturbative framework by taking θ 13 as , which guarantees its validity in a wide range of θ 13 below the Chooz limit. We show on general ground that the correction terms must be of order ϵ 2 . Yet, they nicely fill the mismatch between the approximate and the exact formulas at low energies and relatively long baselines. General theorems are derived which serve for better understanding of δ-dependence of the oscillation probability. Some interesting implications of the large θ 13 hypothesis are discussed.