Prospects for Reconstruction of Leptonic Unitarity Quadrangle and Neutrino Oscillation Experiments

TL;DR

This paper explores how neutrino oscillation experiments can be used to reconstruct the leptonic unitarity quadrangle and measure CP violation, especially considering sterile neutrinos, with a focus on short and long baseline experiments.

Contribution

It analyzes the connection between neutrino survival probabilities and the geometrical parameters of the leptonic unitarity quadrangle, highlighting the potential to measure CP violation in SBL experiments.

Findings

SBL experiments can potentially reconstruct the LUQ and measure CP violation.

LBL experiments are limited to probing only three of the five LUQ parameters.

The presence of sterile neutrinos introduces additional sources of CP violation.

Abstract

After the observation of non-zero $\theta_{13}$ the goal has shifted to observe $CP$ violation in the leptonic sector. Neutrino oscillation experiments can, directly, probe the Dirac $CP$ phases. Alternatively, one can measure $CP$ violation in the leptonic sector using Leptonic Unitarity Quadrangle(LUQ). The existence of Standard Model (SM) gauge singlets - sterile neutrinos - will provide additional sources of $CP$ violation. We investigate the connection between neutrino survival probability and rephasing invariants of the $4\times4$ neutrino mixing matrix. In general, LUQ contain eight geometrical parameters out of which five are independent. We obtain $CP$ asymmetry($P_{\nu_f\rightarrow\nu_{f'}}-P_{\bar{\nu}_f\rightarrow\bar{\nu}_{f'}}$) in terms of these independent parameters of the LUQ and search for the possibilities of extracting information on these independent geometrical parameters in short baseline(SBL) and long baseline(LBL) experiments, thus, looking for constructing LUQ and possible measurement of $CP$ violation. We find that it is not possible to construct LUQ using data from LBL experiments because $CP$ asymmetry is sensitive to only three of the five independent parameters of LUQ. However, for SBL experiments, $CP$ asymmetry is found to be sensitive to all five independent parameters making it possible to construct LUQ and measure $CP$ violation.