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# Tri-bimaximal lepton mixing from symmetry only

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### Abstract

We construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. The horizontal symmetry of our model is based on the permutation group S_3 of the lepton families together with the three family lepton numbers--united this constitutes a symmetry group Delta(6\infty^2). The model makes no predictions for the neutrino masses.

### Most cited references9

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### Finite and Disconnected Subgroups of SU3 and their Application to the Elementary‐Particle Spectrum

(1964)
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### Generation of large flavor mixing from radiative corrections

(2000)
We provide a model independent criterion which would guarantee a large flavor mixing of two quasi-degenerate Majorana neutrinos at the low scale, irrespective of the mixing at the high scale. We also show that such a situation is realizable for a phenomenologically interesting range of parameters of the weak scale theory. We further show that for a similar condition to be implementable for the three generation case, the CP parity of one of the neutrinos needs to be opposite to that of the others.
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### Softly broken lepton numbers and maximal neutrino mixing

,   (2010)
We consider lepton mixing in an extension of the Standard Model with three right-handed neutrino singlets. We require that the three lepton numbers L_e, L_\mu, and L_\tau be separately conserved in the Yukawa couplings, and we assume that they are softly broken only by the Majorana mass matrix M_R of the neutrino singlets. In this framework, where lepton-number breaking occurs at a scale much higher than the electroweak scale, deviations from family-lepton-number conservation are calculable and finite, and lepton mixing stems exclusively from M_R. We then show that a discrete symmetry exists such that, in the lepton mixing matrix U, maximal atmospheric neutrino mixing together with U_{e3}=0 can be obtained naturally. Alternatively, if one assumes that there are two different scales in M_R and that the lepton number \bar L = L_e - L_\mu - L_\tau is conserved in between them, then maximal solar neutrino mixing follows naturally. If both the discrete symmetry and intermediate \bar L conservation are introduced, bimaximal mixing is achieved.
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### Author and article information

###### Journal
28 November 2008
2009-02-24
###### Article
10.1088/1126-6708/2009/04/013
0811.4766

UWThPh-2008-19
JHEP 0904:013,2009
16 pages, no figures; references added, section 3 supplemented by discussion of the group structure of the model
hep-ph