Connecting Leptonic Unitarity Triangle to Neutrino Oscillation with CP Violation in Vacuum and in Matter

TL;DR

This paper introduces a new geometrical interpretation of neutrino oscillation probabilities using the leptonic unitarity triangle (LUT), deriving compact formulas applicable in vacuum and matter, and validating them for long baseline experiments.

Contribution

It presents a novel geometrical framework connecting the LUT to neutrino oscillation probabilities, including matter effects, with simplified formulas for experimental analysis.

Findings

Derived a compact oscillation formula in vacuum using LUT.

Extended the LUT framework to include matter effects.

Validated the formulas against long baseline neutrino experiments.

Abstract

Leptonic unitarity triangle (LUT) provides fundamental means to geometrically describe CP violation in neutrino oscillation. In this work, we use LUT to present a new geometrical interpretation of the vacuum oscillation probability, and derive a compact new oscillation formula in terms of only 3 independent parameters of the corresponding LUT. Then, we systematically study matter effects in the geometrical formulation of neutrino oscillation with CP violation. Including nontrivial matter effects, we derive a very compact new oscillation formula by using the LUT formulation. We further demonstrate that this geometrical formula holds well for applications to neutrino oscillations in matter, including the long baseline experiments T2K, MINOS, NOvA, and DUNE.