Non-standard neutrino oscillations: perspective from unitarity triangles

TL;DR

This paper introduces a geometric approach using unitarity triangles to analyze neutrino oscillations with non-standard interactions, providing a new perspective that simplifies understanding and calculation of oscillation probabilities.

Contribution

It develops a unitarity triangle framework for neutrino oscillations with NSI, offering a geometric and invariant method that simplifies probability expressions and enhances interpretability.

Findings

Derived perturbative expressions for oscillation probabilities with NSI.

Showed the invariance of LUT parameters under rephasing and parameterization.

Identified dependencies of LUT parameters on NSI terms.

Abstract

We formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturbative expansions in the NSI case and make comparisons with approximate expressions existing in literature. We uncover some interesting dependencies on NSI terms while studying the evolution of LUT parameters and the Jarlskog invariant. Interestingly, the geometric approach based on LUT allows us to express the oscillation probabilities for a given pair of neutrino flavours in terms of only three (and not four) degrees of freedom which are related to the geometric properties (sides and angles) of the triangle. Moreover, the LUT parameters are invariant under rephasing transformations and independent of the parameterization adopted.