Predictions for the leptonic Dirac CP violation phase: a systematic phenomenological analysis.

I Girardi,S T Petcov,A V Titov

doi:10.1140/epjc/s10052-015-3559-6

Abstract

We derive predictions for the Dirac phase delta present in the 3times 3 unitary neutrino mixing matrix U = U_e^{dagger } , U_{nu }, where U_e and U_{nu } are 3times 3 unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices. We consider forms of U_e and U_{nu } allowing us to express delta as a function of three neutrino mixing angles, present in U, and the angles contained in U_{nu }. We consider several forms of U_{nu } determined by, or associated with, symmetries, tri-bimaximal, bimaximal, etc., for which the angles in U_{nu } are fixed. For each of these forms and forms of U_e allowing one to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos delta , using (i) the latest results of the global fit analysis of neutrino oscillation data, and (ii) the prospective sensitivities on the neutrino mixing angles. Our results, in particular, confirm the conclusion, reached in earlier similar studies, that the measurement of the Dirac phase in the neutrino mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information as regards the possible existence of symmetry in the lepton sector.

Highlights

Understanding the origin of the observed pattern of neutrino mixing, establishing the status of the CP symmetry in the lepton sector, determining the type of spectrum the neutrino masses obey and determining the nature—Dirac or Majorana—of massive neutrinos are among the highest priority goals of the programme of future research in neutrino physics
We derive predictions for the Dirac phase δ present in the 3 × 3 unitary neutrino mixing matrix U = Ue† Uν, where Ue and Uν are 3 × 3 unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices
In Eq (1) Ue and Uν are CKM-like 3 × 3 unitary matrices, and and Q0 are diagonal phase matrices each containing in the general case two physical CP violation (CPV) phases2:

Summary

Introduction

Understanding the origin of the observed pattern of neutrino mixing, establishing the status of the CP symmetry in the lepton sector, determining the type of spectrum the neutrino masses obey and determining the nature—Dirac or Majorana—of massive neutrinos are among the highest priority goals of the programme of future research in neutrino physics (see, e.g., [1]). The sum rule for cos δ in this case can be obtained with a simpler procedure, namely, by using the expressions for the absolute value of the element Uμ1 of the PMNS matrix in the two parametrisations employed in the present subsection:. We compare the expressions for the absolute value of the element Uτ1 of the PMNS matrix in the standard parametrisation and in the symmetry related one, Eq (17) with θ2ν3 = −π/4 and ω = 0, considered in the present subsection:. To the case considered in the preceding subsection, from the requirements (0 < sin θ1e3 < 1) ∧ (−1 < cos ω < 1) one can obtain for a given θ1ν3, each of the symmetry values of θ1ν2 considered and θ2ν3 = −π/4 lower and upper bounds on the value of sin θ12 These bounds will be discussed in Sect.

Predictions

Summary and conclusions