Z_2 Symmetry Prediction for the Leptonic Dirac CP Phase

TL;DR

This paper derives a model-independent relation linking the Dirac CP phase to neutrino mixing angles under a Z_2 symmetry, predicting near-maximal CP violation, which can be tested in current neutrino experiments.

Contribution

It provides a novel, model-independent formula relating the Dirac CP phase to mixing angles using a Z_2 symmetry, independent of neutrino mass type.

Findings

Delta_D is constrained to be nearly maximal.

The relation is independent of neutrino mass hierarchy.

A lower limit distribution for theta_x is obtained.

Abstract

Model-independent consequences of applying a generalized hidden horizontal Z_2 symmetry to the neutrino mass matrix are explored. The Dirac CP phase delta_D can be expressed in terms of the three mixing angles as 4 c_a s_a c_s s_s s_x cos delta_D = (s^2_s - c^2_s s^2_x) (c^2_a - s^2_a) where the s_i, c_i are sines and cosines of the atmospheric, solar, and reactor angles. This relation is independent of neutrino masses and whether neutrinos are Dirac- or Majorana-type. Given the present constraints on the angles, delta_D is constrained to be almost maximal, a result which can be explored in experiments such as NOvA and T2K. The Majorana CP phases do not receive any constraint and are thus model-dependent. Also a distribution of theta_x with a lower limit is obtained without specifying delta_D.