Leptonic Dirac CP violation predictions from residual discrete symmetries

DOI10.1016/J.NUCLPHYSB.2015.10.020zbMATH Open1332.81252arXiv1509.02502OpenAlexW2107842523MaRDI QIDQ253027

Author name not available (Why is that?)

Publication date: 7 March 2016

Published in: (Search for Journal in Brave)

Abstract: Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group

G_{f}

, and that

G_{f}

is broken to specific residual symmetries

G_{e}

and

G_{u}

of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase

d e l t a

of the neutrino mixing matrix

U

. The residual symmetries considered are: i)

G_{e} = Z_{2}

and

G_{u} = Z_{n}

,

n > 2

or

Z_{n} i m e s Z_{m}

,

n, m g e q 2

; ii)

G_{e} = Z_{n}

,

n > 2

or

Z_{n} i m e s Z_{m}

,

n, m g e q 2

and

G_{u} = Z_{2}

; iii)

G_{e} = Z_{2}

and

G_{u} = Z_{2}

; iv)

G_{e}

is fully broken and

G_{u} = Z_{n}

,

n > 2

or

Z_{n} i m e s Z_{m}

,

n, m g e q 2

; and v)

G_{e} = Z_{n}

,

n > 2

or

Z_{n} i m e s Z_{m}

,

n, m g e q 2

and

G_{u}

is fully broken. For given

G_{e}

and

G_{u}

, the sum rules for

c o s d e l t a

thus derived are exact, within the approach employed, and are valid, in particular, for any

G_{f}

containing

G_{e}

and

G_{u}

as subgroups. We identify the cases when the value of

c o s d e l t a

cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of

c o s d e l t a

can be unambiguously predicted once the flavour symmetry

G_{f}

is fixed. We present predictions for

c o s d e l t a

in these cases for the flavour symmetry groups

G_{f} = S_{4}

,

A_{4}

,

T^{p} r i m e

and

A_{5}

, requiring that the measured values of the 3-neutrino mixing parameters

s i n^{2} h e t a_{12}

,

s i n^{2} h e t a_{13}

and

s i n^{2} h e t a_{23}

, taking into account their respective

3 s i g m a

uncertainties, are successfully reproduced.

Full work available at URL: https://arxiv.org/abs/1509.02502

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