Atsushi WATANABE Niigata Univ amp The MaxPlanckInstitute for Nuclear Physics 23 rd February 2011 HRI Allahabad Based on the work with K Yoshioka Kyoto Univ H Ishimori ID: 398153
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Slide1
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.)Slide2
ContentsSlide3
The bulk right-handed neutrinos
SM
gravity
right-handed
neutrinos
[Dienes,Dudas,Gherghetta,1999]
[Arkani-Hamed,Dimopoulos,Dvali,March-Russell,1999]
Standard Model +
An interesting range of the
n
eutrino mass shows up
Suppressed Dirac mass
Neutrino mass
Slide4
Localization
of the wave function
[Grossman, Neubert, 99]
(SM)
[
Chang,
Hisano
, Nakano, Okada, Yamaguchi
,
99]Slide5
Seesaw in five dimensions
[Dienes,Dudas,Gherghetta,99]
[Lukas, Ramond, Romanino, Ross, 00]
SM
Neutrino mass after the seesawSlide6
Options available in 5D
SM
■
The mass terms (
Majorana
, Dirac, Lorentz-violating …)
■
The bulk geometry (Flat, Warped, Others …)
■
The boundary conditions for the bulk fieldsSlide7
Seesaw with the bulk Dirac mass
[AW, Yoshioka, 2009]
for eV neutrino mass
Bulk DiracSlide8
Inverse seesaw
small
The zero mode function
Zero mode is negligible
in seesaw Slide9
On the warped geometry
Planck (y=0)
TeV
(y=L)
How does the background change the neutrino mass ?Slide10
By the usual KK expansion, …
It is hard to perform seesaw
diagonalizationSlide11
The equations for the bulk propagator
the warped effect is vanishing away at the low-energy limitSlide12
・
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.Slide13
Flavor symmetry breaking at the boundaries
Irreducible representations:
Exmaple
of the
triplet
SM
elements of the
S4
groupSlide14
Lagrangian
of neutrino sectorSlide15
Example I:
・
only one mixing angle
・
degenerate massesSlide16
Example II:Slide17
3 effective parameters:Slide18
Summary
SM
・
Inverse seesaw (bulk Dirac mass)
・
Geometry free nature of the neutrino mass
・
Flavor symmetry breaking
at the boundariesSlide19
Charged-lepton sector
⇒
small mixing for the left-handed direction