higher dimensional seesaw atsushi watanabe niigata univ. & the max-planck-institute for nuclear...
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Higher dimensional seesaw
Atsushi WATANABE
Niigata Univ. & The Max-Planck-Institute for Nuclear Physics
23rd 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 physicsand 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-handedneutrinos
[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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Localization of the wave function[Grossman, Neubert, 99]
(SM)
Dirac (kink) mass in the S1/Z2 bulk
Zero 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]
SM
Neutrino mass after the seesaw
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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
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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
S4 group
Irreducible representations:
Exmaple of the triplet
SM
S4 breaking boundary conditions
elements of the S4group
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Lagrangian of neutrino sector
4D Lagrangian is obtained by
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Example I:
KK expansion
Majorana 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
SM
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