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Higher dimensional seesaw

Higher dimensional seesaw. Atsushi WATANABE. Niigata Univ. & The Max-Planck-Institute for Nuclear Physics. Based on the work with K. Yoshioka (Kyoto Univ.) , H. Ishimori , Y. Shimizu, M. Tanimoto (Niigata Univ.). 23 rd February 2011 @ HRI, Allahabad. Contents. Neutrino mass.

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Higher dimensional seesaw

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  1. Higher dimensional seesaw Atsushi WATANABE Niigata Univ. & The Max-Planck-Institute for Nuclear Physics Based on the work with K. Yoshioka (Kyoto Univ.), H. Ishimori, Y. Shimizu, M. Tanimoto (Niigata Univ.) 23rd February 2011 @ HRI, Allahabad

  2. Contents

  3. Neutrino mass The bulk right-handed neutrinos [Dienes,Dudas,Gherghetta,1999] [Arkani-Hamed,Dimopoulos,Dvali,March-Russell,1999] Standard Model + gravity SM right-handed neutrinos • Suppressed Dirac mass An interesting range of the neutrino mass shows up

  4. (SM) Localizationof the wave function [Grossman, Neubert, 99] [Chang, Hisano, Nakano, Okada, Yamaguchi, 99]

  5. Neutrino mass after the seesaw Seesaw in five dimensions [Dienes,Dudas,Gherghetta,99] [Lukas, Ramond, Romanino, Ross, 00] SM

  6. Options available in 5D SM ■ The mass terms (Majorana, Dirac, Lorentz-violating …) ■ The bulk geometry (Flat, Warped, Others …) ■ The boundary conditions for the bulk fields

  7. for eV neutrino mass Seesaw with the bulk Dirac mass Bulk Dirac [AW, Yoshioka, 2009]

  8. small Inverse seesaw Zero mode is negligible in seesaw The zero mode function

  9. On the warped geometry Planck (y=0) TeV (y=L) How does the background change the neutrino mass ?

  10. By the usual KK expansion, … It is hard to perform seesaw diagonalization

  11. The equations for the bulk propagator the warped effect is vanishing away at the low-energy limit

  12. ・ The neutrino mass is not much affected by the background ・ The result is the same for more general metric ・ The seesaw mass can be calculated without knowing the KK expansion Even with a complicated backgroud where a suitable KK expansion cannot be find, the seesaw neutrino mass is calculable.

  13. Flavor symmetry breaking at the boundaries Irreducible representations: Exmaple of the triplet elements of the S4 group SM

  14. Lagrangian of neutrino sector

  15. Example I: ・ only one mixing angle ・ degenerate masses

  16. Example II:

  17. 3 effective parameters:

  18. Summary SM ・ Inverse seesaw (bulk Dirac mass) ・ Geometry free nature of the neutrino mass ・ Flavor symmetry breaking at the boundaries

  19. Charged-lepton sector ⇒ small mixing for the left-handed direction

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