in collaboration with h. ishida (niigata university...
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1Erice 2009 (Erice-Sicily, 14-24 September 2009) 1
@ Erice-Sicily, 20 September, 2009In collaboration with H. Ishida (Niigata University)Takehiko Asaka(Niigata U)
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νν
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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9(10 )GeVMM O> ( )MTiny ν masses [Fukugita, Yanagida ’86] νν
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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9(10 )GeVMM O> ( )MTiny ν masses [Fukugita, Yanagida ’86] νν
2(10 )GeVMM O<Very small Y k li ν [Akhmedov, Rubakov, Yukawa couplings Smirnov ’98]Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
ν 5[TA, Shaposhnikov ’05] 5 1 2 3( , , )N N N
. .2
cII I I I I I
ML iN N F L N N N h cμμ α αγ= ∂ − Φ − +
[ ] and [ ] ( , , ; 1, 2,3)D I I M II IM F M M e Iα α α μ τ= Φ = = =
2| | (10 )GeVD I IM M Oα <
1/41/2 2
1 TD M DM M M Mν
−= −1/41/2 2
83 24 10
GeV 2.5 10 eVI mM
F ν−−
× ×
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
66221 /T
D D MM M M F M M H= − = /D D MM
M M M F M M HMν ν
2a
2M Δ10-2
100
102
ukawa
F = Ft
2atmM mν = Δ
10-6
10-4
10-2
no Yu
F = Fe
10-10
10-8
10-6
utrin
10-14
10-12
10
Neu
10
10-10 10-5 100 105 1010 1015
Majorana Mass [GeV]
2009/04/22(Wed)Takehiko Asaka (Niigata Univ.)
7(“Dark” sterile neutrino) 71N
1 0Fα ≈
(“Bright” and “Clear” sterile neutrinos)2 3 and N N
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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[Akh d R b k S i ’98][Akhmedov, Rubakov, Smirnov ’98][TA, Shaposhnikov ’05]
MMTakehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
1010
•
• st• st•
•
• MTakehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
1111
sphaleron
sphaleron2,3N2,3Np
, ,eL μ τ, ,eL μ τ
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
2 1212
Lα N2,3
ΦtR QL
2 1/332( )L plT T M M= Δ
N2
p
N2
N3N NL
F †F
2†
8NTV F Fk
=N3 F †FMedium effects
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
4 13[TA, Shaposhnikov ‘05] 13
N2,3Lα
L0, 0, 0 eL L Lμ τΔ ≠ Δ ≠ Δ ≠
Lαμ
L LN
Lα LαL LN
†F F
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
6 14
14
N LΔIN eLΔ
LμΔ tot 2 3 0N N NΔ = Δ + Δ ≠
INμ
LτΔ tot 0 eL L L Lμ τΔ = Δ + Δ + Δ ≠
N NL
F †FIN IN
LΔ F †FLαΔ
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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2 1/332( ) 2.2TeVL plT M MΔ =
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
1616totLΔ
28[Kuzmin, Rubakov, Shaposhnikov ‘85]
tot28 079
B LΔ = − Δ ≠
4tot7.0 10
W
BT T
n L−=
= − × Δ
11(8 81 0 23) 10Bn −± ×
0WT Ts =
2 2TeVT = 100GeVTobs
(8.81 0.23) 10B
s= ± ×2.2TeVLT = 100GeVWT =
3 3GeVM = 2 2 82 3 (1 10 )M M −= −
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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[TA I hid i i ][TA, Ishida in preparation]dN N2 3 and N N
[ ] [ ]M M β 11n
2,3
[ ] [ ][ ] D I D I
I I
M MM
Mα β
ν αβ=
= − 11
obs
(8.81 0.23) 10Bns
−= ± ×
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
18181/2 1/2
PMNS /NF U D Dν= Ω Φ[Casas, Ibarra ’01]
S Nν
δ1 2 3
1/2 diag( , , )D m m mν =
12 13 12 13 13 1ic c s c s e δ−
: active ν masses δ
12 13 12 13 13
PMNS 23 12 23 12 13 23 12 23 12 13 23 13
23 12 23 12 13 23 12 23 12 13 23 13 1
i i i
i i
U c s s c s e c c s s s e s c e
s s c c s e s c c s s e c c
δ δ φ
δ δ
= − − −
− − −
23 12 23 12 13 23 12 23 12 13 23 13
φ2 3
1/2 diag( , )ND M M=
0 0
: sterile ν masses: complex numberω
cos sin
sin cos
ω ωω ωξ ξ
Ω = −
p1ξ = ±
ω
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)ω
19[Akhmedov, Rubakov, Smirnov ’98]19 2,3: density matrix for NN Nρ
{ }0 , ,2
d eqNNNN N NN NN NN NN
d ii H Vdtρ ρ ρ ρ = + − Γ −
2†
8NTV F Fk
= 0.04 dN NVΓ
† 1/2 † 1/2N NF F D D Dν= Ω Ω
PMNSU
PMNS
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
2020 [TA, Shaposhnikov ’05]
N NL L LNN NLF †F †F FF F F F
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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[TA, Shaposhnikov ’05]{ } †0 , ,
2sin ( )
4eq
LLd eqNN
NN N NN NN NN LLNNd ii H V
dti T F Fρ ρ ρ φ ρ ρρ + ⋅ − = + − Γ −
{ }0 †sin[ , ] , + ( )2 4
diagdiag d diag eq eqLL
LL L LL LL LL LL NN NNd i ii H V T F F
dtρ φρ ρ ρ ρ ρ= + − Γ − ⋅ −
PMNSU
PMNSU
δ φδ φ Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
δ 22φ 2213sin 0.2θ =
BAU BAUDirac phase 13sinθ
0 0
12 13 12 13 13 1ic c s c s e δ−
Dirac phase 13
cos sin
sin cos
ω ωω ωξ ξ
Ω = −
PMNS 23 12 23 12 13 23 12 23 12 13 23 13
23 12 23 12 13 23 12 23 12 13 23 13 1
i i i
i i
U c s s c s e c c s s s e s c e
s s c c s e s c c s s e c c
δ δ φ
δ δ
= − − −
− − −
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
232311(8 81 0 23) 10Bn −= ± ×
obs
(8.81 0.23) 10s
± ×
hase 3 3GeVM =
oranaph
i 0 2θ
3 3GeVM2 2 82 3 (1 10 )M M −= −
Majo 13sin 0.2θ =
0 0
cos sinω ωΩ Dirac phase cos sin
sin cos
ω ωω ωξ ξ
Ω = −
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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M 9 M
M 2
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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2 2 23 2 1, , 0atm sol solm m m m m m= Δ + Δ = Δ =
2 3 2
2 5 2
2.5 10 eVatmm −Δ = ×2 5 28.0 10 eVsolm −Δ = ×
23 12/ 4, / 5θ π θ π= = 13sin 0.2θ ≤
, δ φ
2 2 82 2 83 2 33GeV, (1 10 )M M M −= = −
Re Imω ω ω= +Re Imω ω ω= +
1ξ = ±ξ
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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: complex numberω1ξ = ±
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)
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Normal hierarchy
Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)