Fully Constrained Majorana Neutrino Mass Matrices Using $\Sigma(72\times 3)$

Krishnan, R.; Harrison, P.F.; Scott, W.G.

doi:10.1140/epjc/s10052-018-5516-7

Fully Constrained Majorana Neutrino Mass Matrices Using $\Sigma(72\times 3)$

Jan 25, 2018

20 pages

Published in:

Eur.Phys.J.C 78 (2018) 1, 74

Published: Jan 25, 2018

e-Print:

1801.10197 [hep-ph]

DOI:

10.1140/epjc/s10052-018-5516-7

View in:

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Abstract: (Springer)

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (

\nu _2

) columns, namely tri-chi-maximal mixing (

\text {T}\chi \text {M}

) and tri-phi-maximal mixing (

\text {T}\phi \text {M}

), were proposed. In 2012, it was shown that

\text {T}\chi \text {M}

with

\chi =\pm \,\frac{\pi }{16}

as well as

\text {T}\phi \text {M}

with

\phi = \pm \,\frac{\pi }{16}

leads to the solution,

\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}

, consistent with the latest measurements of the reactor mixing angle,

\theta _{13}

. To obtain

\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}

and

\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}

, the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios,

m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}

. In this paper we construct a flavour model based on the discrete group

\varSigma (72\times 3)

and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric

3\times 3

matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of

\varSigma (72\times 3)

. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

Note:

20 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0857

neutrino: Majorana: mass
neutrino: mass
neutrino: Majorana
neutrino: mixing
neutrino: mass ratio
group: discrete
flavor: model
dimension: 6
flavon
nuclear reactor

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Fully Constrained Majorana Neutrino Mass Matrices Using Σ(72×3)\Sigma(72\times 3)Σ(72×3)

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Fully Constrained Majorana Neutrino Mass Matrices Using $\Sigma(72\times 3)$