Magic baseline and magic energy in neutrino oscillation with non-standard interactions

TL;DR

This paper explores conditions under which neutrino oscillation probabilities are independent of CP violation, introducing an energy-based 'magic' condition that complements the known baseline condition, with implications for hierarchy resolution and experimental measurements.

Contribution

It proposes an energy-based 'magic' condition for neutrino oscillations with non-standard interactions, expanding the scenarios where CP phase independence can be achieved.

Findings

Magic baseline condition is not always feasible, especially with non-standard interactions.

Energy condition can be applied in cases where baseline condition fails.

Potential to resolve neutrino mass hierarchy using the energy condition.

Abstract

We have discussed conditions under which probability of oscillation ($\nu_e\rightarrow \nu_{\mu}$) is independent of CP violating phase $\delta$. The condition of magic baseline on its length is well-known. We have proposed another condition which is on neutrino energy. We have shown that magic baseline condition is not possible in general, for small $\theta_{13}$ with non-standard interaction and for large $\theta_{13}$ with both standard and non-standard interactions. However, neutrino energy condition is possible for such cases as well as for cases where magic baseline condition is applicable. We have discussed how one may resolve hierarchy problem for neutrino masses by using such energy condition. For a baseline of length 650 Km, using this energy condition we discuss the possible number of $\mu^-$ events at the detector for a period of 5 years and also the sensitivity in measurement of $\cos^2 \theta_{13}$.