CP nonconservation in the leptonic sector

TL;DR

This paper proposes a novel global fit method using unitarity constraints and convention-independent parameters to determine CP violation in the leptonic sector from neutrino data.

Contribution

It introduces a new approach to analyze neutrino mixing data by expressing parameters in a way that resolves positivity issues and directly estimates the CP violation measure J.

Findings

Potential detection of CP violation if J is non-zero

Method can indicate new physics if |U_{e3}|^2<0 is confirmed

Provides a framework for analyzing limited experimental data

Abstract

In this paper we use an exact method to impose unitarity on moduli of neutrino PMNS matrix recently determined, and show how one could obtain information on CP nonconservation from a limited experimental information. One suggests a novel type of global fit by expressing all theoretical quantities in terms of convention independent parameters: the Jarlskog invariant $J$ and the moduli $|U_{\alpha i}|$, able to resolve the positivity problem of $|U_{e 3}|$. In this way the fit will directly provide a value for $J$, and if it is different from zero it will prove the existence of CP violation in the available experimental data. If the best fit result, $|U_{e3}|^2<0$, from M. Maltoni {\em et al}, [New J.Phys. {\bf 6} (2004) 122] is confirmed, it will imply a new physics in the leptonic sector.