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 \equiv Delta m^2_{ 21} / Delta m^2_{ 31} \simeq 0.03 under the assumption s_{ 13} \simeq epsilon. If theta_{ 13} is large, as suggested by a candidate nu_{ 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} \sim \sqrt{ epsilon} \simeq 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.
Categories: hep-ph