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.
Highlights
JHEP05(2021)171 density, obtaining analytical expressions of oscillation probabilities in presence of non-standard interactions (NSI) is a cumbersome exercise
The accuracy of the leptonic unitarity triangle (LUT) expression for the neutrino oscillation probability with standard matter interactions given by eq (2.11) with respect to the exact numerical calculation was tested in ref. [46] for different baselines ranging between 295 − 1300 km
We have formulated an alternative approach based on the LUT to describe neutrino oscillations in the presence of non-standard neutrino interactions with matter
Summary
Three-generation neutrino mixing can be described by a 3 × 3 unitary mixing matrix U , which appears in the weak charged current interactions. Where sij = sin θij, cij = cos θij and δ is the Dirac-type CP phase. If neutrinos are Majorana particles, there can be two additional Majorana-type phases in the three flavour case, as U → U diag(1, eiκ, eiζ). These Majorana phases play no role in neutrino oscillation studies as they give rise to an overall phase in the neutrino oscillation amplitude which is not measurable. Since we are interested in neutrino flavour oscillations, we will consider only the Dirac LUT, as shown in figure 1(a). 1ντ appearance has been discussed in the context of the upcoming DUNE experiment in [51,52,53,54]
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