Exact and Approximate Formulas for Neutrino Mixing and Oscillations with Non-Standard Interactions

TL;DR

This paper derives exact and approximate formulas linking vacuum and matter neutrino mixing parameters considering non-standard interactions, aiding future long-baseline neutrino oscillation experiments.

Contribution

It provides a complete set of mappings and sum rules for neutrino mixing parameters in matter with NSI effects, including compact approximate formulas for practical use.

Findings

Effective mixing parameters are reconstructed from vacuum parameters.

NSIs significantly influence the mixing angle  and transition probabilities.

Approximate formulas are highly accurate for experimental predictions.

Abstract

We present, both exactly and approximately, a complete set of mappings between the vacuum (or fundamental) leptonic mixing parameters and the effective ones in matter with non-standard neutrino interaction (NSI) effects included. Within the three-flavor neutrino framework and a constant matter density profile, a full set of sum rules is established, which enables us to reconstruct the moduli of the effective leptonic mixing matrix elements, in terms of the vacuum mixing parameters in order to reproduce the neutrino oscillation probabilities for future long-baseline experiments. Very compact, but quite accurate, approximate mappings are obtained based on series expansions in the neutrino mass hierarchy parameter \eta \equiv \Delta m^2_{21}/\Delta m^2_{31}, the vacuum leptonic mixing parameter s_{13} \equiv \sin\theta_{13}, and the NSI parameters \epsilon_{\alpha\beta}. A detailed numerical analysis about how the NSIs affect the smallest leptonic mixing angle \theta_{13}, the deviation of the leptonic mixing angle \theta_{23} from its maximal mixing value, and the transition probabilities useful for future experiments are performed using our analytical results.