Large-Theta(13) Perturbation Theory of Neutrino Oscillation for Long-Baseline Experiments

TL;DR

This paper develops a systematic perturbation framework for neutrino oscillation probabilities, incorporating large theta_{13} effects, and improves the accuracy of existing formulas for long-baseline experiments.

Contribution

It introduces a new perturbative approach that accounts for large theta_{13}, extending the validity of oscillation probability formulas beyond previous approximations.

Findings

Correction terms are of order epsilon^2.

The new formulas better match exact calculations at low energies.

Implications of large theta_{13} for oscillation analysis are discussed.

Abstract

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.