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

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Contents The interplay between neutrino physics and the extra dimensions The bulk right-handed neutrinos KK expansion and the propagator Flavor symmetry breaking on orbifolds

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

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Localizationof the wave function Localization of the wave function [Grossman, Neubert, 99] (SM) Dirac (kink) mass in the S1/Z2 bulkZero mode function [Chang, Hisano, Nakano, Okada, Yamaguchi, 99]

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

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

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

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Inverse seesaw small The zero mode function Zero mode is negligible in seesaw Whole neutrino mass matrix

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On the warped geometry Randall-Sumdrum background Planck (y=0)TeV (y=L) How does the background change the neutrino mass ?

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

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The equations for the bulk propagator the warped effect is vanishing away at the low-energy limit Alternative to the KK expansion ⇒ 5D propagator

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The result is ・ 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.

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Flavor symmetry breaking at the boundaries S 4 group Irreducible representations: Exmaple of the triplet S 4 breaking boundary conditions elements of the S4 group

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Lagrangian of neutrino sector 4D Lagrangian is obtained by

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Example I: KK expansionMajorana mass matrix after the seesaw ・ only one mixing angle ・ degenerate masses

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Example II: The result is

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3 effective parameters: Deviation from the tri-bimaximal mixing

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Summary We have explored ``bulk seesaw” ・ Inverse seesaw (bulk Dirac mass) ・ Geometry free nature of the neutrino mass ・ Flavor symmetry breaking at the boundaries

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Charged-lepton sector For Example ⇒ small mixing for the left-handed direction

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