Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay · arXivDesk
1605.04172May 13, 201659 pages, includes 8 figures and 6 tables; a discussion of the effects of the uncertainties in the values of neutrino mixing angles on the predictions for the Majorana phases and four new related figures (two in the main text and two in a new appendix) added
Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay
We obtain predictions for the Majorana phases α21/2 and α31/2 of the 3×3
Nearby in the stack
unitary neutrino mixing matrix
U=Ue†Uν
,
Ue
and
Uν
being the
3×3
unitary matrices resulting from the diagonalisation of the charged lepton and neutrino Majorana mass matrices, respectively. We focus on forms of
Ue
and
Uν
permitting to express
α21/2
and
α31/2
in terms of the Dirac phase
δ
and the three neutrino mixing angles of the standard parametrisation of
U
, and the angles and the two Majorana-like phases
ξ21/2
and
ξ31/2
present, in general, in
Uν
. The concrete forms of
Uν
considered are fixed by, or associated with, symmetries (tri-bimaximal, bimaximal, etc.), so that the angles in
Uν
are fixed. For each of these forms and forms of
Ue
that allow to reproduce the measured values of the three neutrino mixing angles
θ12
,
θ23
and
θ13
, we derive predictions for phase differences
(α21/2−ξ21/2)
,
(α31/2−ξ31/2)
, etc., which are completely determined by the values of the mixing angles. We show that the requirement of generalised CP invariance of the neutrino Majorana mass term implies
ξ21=0
or
π
and
ξ31=0
or
π
. For these values of
ξ21
and
ξ31
and the best fit values of
θ12
,
θ23
and
θ13
, we present predictions for the effective Majorana mass in neutrinoless double beta decay for both neutrino mass spectra with normal and inverted ordering.