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 epsilon Delta m(2)(21)/Delta m(31)(2) similar or equal to 0.03 under the assumption s(13) similar or equal to epsilon. If theta(13) is large, as suggested by a candidate v(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 theta(13) as s(13) similar to root epsilon similar or equal to 0.18, which guarantees its validity in a wide range of theta(13) below the Chooz limit. We show on general ground that the correction terms must be of order epsilon(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 delta-dependence of the oscillation probability. Some interesting implications of the large theta(13) hypothesis are discussed.