Connecting leptonic unitarity triangle to neutrino oscillation

Abstract

The leptonic unitarity triangle (LUT) provides a geometric description of $CP$ violations in the lepton-neutrino sector and is directly measurable in principle. In this paper, we reveal that the angles in the LUT have definite physical meaning, and demonstrate the exact connection of the LUT to neutrino oscillations. For the first time, we prove that these leptonic angles act as phase shifts in neutrino oscillations, by shifting $\mathrm{\ensuremath{\Delta}}{m}^{2}L/2E$ to $\mathrm{\ensuremath{\Delta}}{m}^{2}L/2E+\ensuremath{\alpha}$, where $(L,E,\ensuremath{\alpha})$ denote the baseline length, neutrino energy and corresponding angle of the LUT. Each LUT has three independent parameters and contains only partial information of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix. We demonstrate that the partial information in each LUT can describe the corresponding neutrino oscillation. Hence, for the first time, we uncover that any given kind of neutrino oscillations contains at most three (rather than four) independent degrees of freedom from the PMNS matrix, and this may provide a cleaner way for fitting the corresponding oscillation data.