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Obtaining a nonzero 13 in lepton models based on SO(3) A 4 Yuval Grossman and Wee Hao Ng, Cornell University Phenomenology 2014 arXiv:1404.1413 [hep-ph] 1

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Outline Tri-bimaximal mixing found and lost; how do A 4 models cope? Basics of SO(3) A 4 model Nonzero 13 in SO(3) A 4 model Summary 2

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Tri-bimaximal mixing and A 4 models For long time, PMNS matrix thought to be consistent with TBM Highly specific pattern… discrete lepton flavor symmetries? 3

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Tri-bimaximal mixing and A 4 models Simplest A 4 lepton models – Components SM Higgs and leptons Right handed neutrinos Scalar flavons , ’ – Features Additional Z 2 symmetry so flavons sectorized Flavons gain VEV = (v, v, v), ’ = (v’, 0, 0) Representations of A 4 TBM! 4

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Tri-bimaximal mixing… lost Recently, 13 found to be much larger! Daya Bay (2012): RENO (2012): TBM ruled out! 5

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How do A 4 models cope? Actually many A 4 models already allow this! Approaches: – Higher dimension operators, e.g. [Altarelli and Meloni (2009)] – More flavons, e.g. [Chen et al (2013)] – Perturb flavon alignments, e.g. [King (2011)] – Radiative corrections, e.g. [Antusch et al (2003)] 6

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Continuous symmetry A 4 Class of models based on continuous symmetry A 4. Originally motivated to explain origin of A 4. Specific example: SO(3) A 4 [Berger and Grossman (2009)] Turns out 13 already nonzero at tree level! Even better: 13 related to 7

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Basics of SO(3) A 4 model Left-handed leptons Right-handed leptons Scalars 8

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Basics of SO(3) A 4 model Most general Lagrangian for leptons Flavons gain VEV 6 6 mass matrices 9 3D coordinate basis vectors

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Obtaining U PMNS U PMNS characterize charged-current interactions between light eigenstates. 6 6 mass matrices: – Block-diagonalise 6 6 mass matrices. – Then diagonalise 3 3 mass matrices. Neutrinos: 10

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Obtaining U PMNS Charged leptons: 11

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Nonzero 13 Block diagonalize Useful to define Then Expanding in small parameter – LO: – NLO: 13 still 0! Suggests 13 ~ ! 12

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Nonzero 13 Actual contribution to 13 from deviation turns out to be ~ (m /m ) ~ 10 Random simulation results In agreement with predictions! 13

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Summary and further work TBM ruled out, but many A 4 models allow for this scenario In particular, SO(3) A 4 model allow nonzero tree-level 13 of size % level separation of A 4 and SO(3) breaking scales 14

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Thank you! 15

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