In collaboration with H. Ishida (Niigata University...

1Erice 2009 (Erice-Sicily, 14-24 September 2009) 1

@ Erice-Sicily, 20 September, 2009In collaboration with H. Ishida (Niigata University)Takehiko Asaka(Niigata U)

22

νν

Takehiko Asaka (Niigata U) Erice 2009 (Erice-Sicily, 14-24 September 2009)

33

9(10 )GeVMM O> ( )MTiny ν masses [Fukugita, Yanagida ’86] νν


44

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−−

× ×


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


88


99

[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


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


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


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


1515

2 1/332( ) 2.2TeVL plT M MΔ =


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 −= −


1717

[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

−= ± ×


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


2020 [TA, Shaposhnikov ’05]

N NL L LNN NLF †F †F FF F F F


2121

[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

= − − −

− − −


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 = −


2424

M 9 M

M 2


2525

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


2626

: complex numberω1ξ = ±


2727

Normal hierarchy


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