Fully Constrained Mass Matrix: Can Symmetries alone determine the Flavon Vacuum Alignments? - INSPIRE

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Fully Constrained Mass Matrix: Can Symmetries alone determine the Flavon Vacuum Alignments?

R. Krishnan
(
- Unlisted, IN
)

Jan 4, 2019

18 pages

Published in:

Phys.Rev.D 101 (2020) 7, 075004

Published: Apr 4, 2020

e-Print:

1901.01205 [hep-ph]

DOI:

10.1103/PhysRevD.101.075004

View in:

ADS Abstract Service

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Abstract: (APS)

In the framework of the representation theory of finite groups, it was recently shown that a fully constrained complex-symmetric mass matrix can be conveniently mapped into a sextet of Σ(72×3). In this paper, we introduce an additional flavor group X24 in the model so that the vacuum alignment of the Σ(72×3) sextet is determined not only by the symmetries of Σ(72×3) but also by that of X24. We define several flavons which transform as multiplets under Σ(72×3) as well as X24. The vacuum alignment of each of these flavons is obtained as a simultaneous invariant eigenstate of specific elements of the groups Σ(72×3) and X24; i.e., the vacuum alignment is fully determined by its residual symmetries. These flavons couple together uniquely resulting in the fully constrained sextet of Σ(72×3). Through this work we propose a general formalism in which the flavor symmetry group (Gf) is obtained as the direct product, Gf=Gr×Gx. Fermions transform nontrivially only under Gr while they remain invariant under Gx. Flavons, on the other hand, transform nontrivially under both Gr and Gx. The vacuum alignment of each flavon multiplet transforming irreducibly under Gr×Gx is uniquely identified by its corresponding residual symmetry (a subgroup of Gr×Gx). Several such flavons couple together to form an effective multiple of Gr which remains invariant under Gx. This effective multiplet couples to the fermions.

Note:

17 pages, 3 figures

14.60.Pq
11.30.Hv
Beyond the standard model
mass: constraint
group: finite
symmetry: flavor
neutrino: Majorana: mass
flavon
vacuum state: alignment
sextet

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