1 / 15

Obtaining a nonzero  13 in lepton models based on SO(3)  A 4

Obtaining a nonzero  13 in lepton models based on SO(3)  A 4. Yuval Grossman and Wee Hao Ng , Cornell University. arXiv:1404.1413 [ hep -ph]. Phenomenology 2014. Outline. Tri- bimaximal mixing found and lost; how do A 4 models cope? Basics of SO(3)  A 4 model

evita
Download Presentation

Obtaining a nonzero  13 in lepton models based on SO(3)  A 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Obtaining a nonzero 13 in lepton models based on SO(3)  A4 Yuval Grossman and Wee Hao Ng, Cornell University arXiv:1404.1413 [hep-ph] Phenomenology 2014

  2. Outline • Tri-bimaximal mixing found and lost; how do A4 models cope? • Basics of SO(3)  A4 model • Nonzero 13 in SO(3)  A4 model • Summary

  3. Tri-bimaximal mixing and A4 models • For long time, PMNS matrix thought to be consistent with TBM • Highly specific pattern… discrete lepton flavor symmetries?

  4. Tri-bimaximal mixing and A4 models • Simplest A4 lepton models • Components • SM Higgs and leptons • Right handed neutrinos • Scalar flavons, ’ • Features • Additional Z2 symmetry so flavonssectorized • Flavons gain VEV  = (v, v, v), ’ = (v’, 0, 0) Representations of A4  TBM!

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

  6. How do A4 models cope? • Actually many A4 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)]

  7. Continuous symmetry  A4 • Class of models based on continuous symmetry  A4. • Originally motivated to explain origin of A4. • Specific example: SO(3)  A4 [Berger and Grossman (2009)] • Turns out 13 already nonzero at tree level! • Even better: 13 related to

  8. Basics of SO(3)  A4 model Left-handed leptons Right-handed leptons Scalars

  9. Basics of SO(3)  A4 model • Most general Lagrangian for leptons • Flavons gain VEV 3D coordinate basis vectors  6  6 mass matrices

  10. Obtaining UPMNS • UPMNS characterize charged-current interactions between light eigenstates. • 6  6 mass matrices: • Block-diagonalise6  6 mass matrices. • Then diagonalise 3  3 mass matrices. • Neutrinos:

  11. Obtaining UPMNS • Charged leptons:

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

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

  14. Summary and further work • TBM ruled out, but many A4 models allow for this scenario • In particular, SO(3)  A4 model allow nonzero tree-level 13 of size • % level separation of A4 and SO(3) breaking scales

  15. Thank you!

More Related