21 Sept. 20051
The The MSMMSM-- Neutrino Masses and Dark matter ---- Neutrino Masses and Dark matter --
Takehiko Asaka (Tohoku University)
TA, S.Blanchet, M.Shaposhnikov [hep-ph/0503065]TA, M.Shaposhnikov [hep-ph/0505013]
21 Sept. 2005 2
Neutrino oscillations
The MSM contradicts with oscillation experiments!!
– Solar, atmospheric, reactor and accelerator experiments
– Neutrino mass scales:
A simplest extension including neutrino masses is
2 3 22.2 10 eVatmm 2 5 28.2 10 eVsolm
21 Sept. 2005 3
Neutrino oscillations
The MSM contradicts with oscillation experiments!!
– Solar, atmospheric, reactor and accelerator experiments
– Neutrino mass scales:
A simplest extension including neutrino masses is
2 3 22.2 10 eVatmm 2 5 28.2 10 eVsolm
The MSM
21 Sept. 2005 4
What is the MSM?
The MSM + Several right-handed neutrinos
– Dirac masses and Majorana masses
– If Dirac masses << Majorana masses,
the seesaw mechanism works
+ h.c.2
cII I I I I I
ML iN N F L N N N
( 1, 2, )IN I
Not new!!!
DM F
Minkowski ’77, Yanagida ’79, Gell-Mann, Ramond, Slansky ’79Glashow ‘79
IM
21 Sept. 2005 5
Seesaw mechanism
If Dirac masses << Majorana masses,
The mixing in the charged current
0 0
0D
TMD M
M
M
M
M M
1TD D
M
M M MM
acIa IU N ( ) / 1I D I IM M
• Active neutrinos
• Sterile neutrinos
1 3 1 2 32 , , ( )m m m
1 2 1 2 (, ) ,N N M M
1 2 3( , , )TU M U diag m m m
1 2 3( , , )MM diag M M M
( , , )e ( 1,2,3)a
21 Sept. 2005 6
Scale of the MSM
What are the scales of Majorana masses??2 2 2/ /M DM M M F M
1TD D
M
M M MM
2atmM m
21 Sept. 2005 7
Conventional approach
F ~ Yukawa couplings in quarks and charged leptons
The new energy scale is introduced
• Can explain neutrino oscillations• Can explain baryon asymmetry of the universe via “leptogenesis” Fukugita and Yanagida ‘86
10 1510 10 GeVMM
21 Sept. 2005 8
Approach here
Majorana masses are weak scale (~100GeV) or below
No new energy scale is introduced
• Can explain neutrino oscillations• Can explain baryon asymmetry of the universe via neutrino oscillations• Can explain dark matter of the universe
Very small neutrino Yukawa couplings
21 Sept. 2005 9
In this talk
Q. How many right-handed neutrinos are required?
A. Minimal possibility is “three”!!
•Neutrino Osc. The minimal # is “two”•Neutrino Osc. + Baryon Asymmetry “two”•Neutrino Osc. + Baryon Asymmetry + Dark Matter “three”
2 2, atm solm m
21 Sept. 2005 10
Dark matter in the universe
Contents of the universe:
The MSM cannot offer a particle physics candidate for dark matter (DM)!!
73%
4%b
2 0.0080.0090.113dmh
Baryon
PDG
Dark EnergyDark Matter
23%dm
21 Sept. 2005 11
Dark matter in the MSM
The unique candidate:
The allowed mass range is (see later discussion)
Long-lived sterile neutrinosPeebles ’82, Olive, Turner ’82Dodelson, Widrow ’94, Shi, Fuller ’99Dolgov, Hansen ’00, Abazajian, Fuller, Patel ‘01
2keV 5keVMM
Sterile neutrinos as “warm dark matter”
• Hot dark matter of active massive neutrinos is excluded by the LSS and CMBR 2 34.5 10h
21 Sept. 2005 12
Lifetime of sterile neutrinos
When Yukawa couplings are very small,
sterile neutrinos can be very long-lived!!
Main decay cannel:
Lifetime can exceed the age of universe
3IN 5 8
262
1keV 105 10 sec
| |IM
1710 sec
/D IM M
Barger, Phillips, Sarkar ‘95
21 Sept. 2005 13
Production of sterile neutrinos
When Yukawa couplings are very small,
sterile neutrinos are not thermalized
Main production is due to the scatterings
at
Dirac mass is determined !
222
8, ,
| |0.1
10 1keVI I
NI e
Mh
2 20
, ,
| ( ) | ,D II e
M m
0 (0.1)eVm O
1/3100MeV /1keVIT M
TA, Blanchet, Shaposhnikov ‘05
Dolgov, Hansen ’00, Abazajian, Fuller, Patel ‘01
/D IM M
21 Sept. 2005 14
Cosmological constraints
Radiative decays of DM sterile neutrinos
are limited by X-ray observations
Warm dark matter is limited by structure formation– WMAP + Matter power spectrum inferred from Ly- forest
Only a small window is left
5keVIM Abazajian, Fuller, Tucker ‘01
2keVIM Viel, Lesgourgues, Haehnelt, Matarrese, Riotto ‘05
2keV 5keVIM
21 Sept. 2005 15
Implications of DM sterile neutrinos
Dark matter constraints:
Consistency with oscillation experiments lead to
The point is
2keV 5keV,IM 22 2
0| ( ) | [ (0.1)eV]D II
M m O
25 2 20 (10 )eVdm
sol atmI
mm O m m
M
• The minimal number of sterile neutrinos is “three”• Only ”one” sterile neutrino can be dark matter• The lightest active neutrino mass is m1<O(10-5)eV
TA, Blanchet, Shaposhnikov ‘05
25 10 eV39 10 eV
21 Sept. 2005 16
Seesaw mass matrix
Parameterization
The following arguments is based on calculating the trace and determinant of (XX)
1 2 3( , , )diag TM diag m m m U M U
1TD D
M
M M MM
( ) /Ia D Ia IX M U M1 1 2 2( ) ( )ab abX X X X
Note: det( ) det( ) 0I I I I J JX X X X X X
Independent on the neutrino mixing matrix U!!!
21 Sept. 2005 17
The MSM with two sterile neutrinos
Active masses:
When both sterile neutrinos are DM, …
1 0m
2 23 5 10 eVatmm m
2 2 32 (NH), 9 10 eV(IH)atm solm m m
1 1 2 2 ,diagM X X X X 2 5
1,2 1
| | (10 )eVdmIIa
I a
MX m O
M
2 22 3 1 2(tr( ))diag
a aa
m m XM X 2 2
1 2(| | | | ) dma a
a
X X m
Contradiction !!
21 Sept. 2005 18
The MSM with two sterile neutrinos
Active masses:
When one sterile neutrino is DM, …
1 0m
2 23 5 10 eVatmm m
2 2 32 (NH), 9 10 eV(IH)atm solm m m
1 1 2 2 ,diagM X X X X 2 2 5
11 1
| | | | (10 )eVdmIIa a
I a a
MX X m O
M
Contradiction !!
2 2det( ) 0 X X
2 212 13| | | | dmX X m 2 22
2 12 133
mm X X
m
1 1det( ) 0diagM X X
11 0X
21 Sept. 2005 19
The MSM with three sterile neutrinos
We can similarly exclude the cases in which
two and three sterile neutrinos are dark matter
When one sterile neutrino is dark matter,…
2 2 3 3det( ) 0 X X X X
2 2 211 12 13| | | | | | dmX X X m
Upper bound on the lightest active neutrino mass !!
2 2 21 11 11 12 13
2 3
m mm X X X
m m
1 1 2 2 3 3 ,diagM X X X X X X 2 51| | (10 )eVdma
a
X m O
1 1det( ) 0diagM X X
21 Sept. 2005 20
Masses of active neutrinos
We can determine the absolute values of active masses
51 (10 )eVdmm m O
21 Sept. 2005 21
Test for DM sterile neutrino
Radiative decays of DM sterile neutrinos may be seen in X-ray observations!!
The current status
The future experiments will detect or exclude the sterile neutrino dark matter.
5keV eV2 kIM
X-rayCMBR+Ly-
Abazajian, Fuller, Tucker ‘01
21 Sept. 2005 22
Summary
We discussed the extension of the MSM
by adding several right-handed neutrinos -The MSM- Only particle physics candidate for dark matter is
long-lived sterile neutrino
– The minimal number of RH neutrinos is three
– Only one sterile neutrino can be dark matter
– The lightest active neutrino mass
The absolute values of active masses are determined The DM sterile neutrinos may be tested in the future X-
ray observations
51 (10 )eVdmm m O
21 Sept. 2005 23
Conclusions
We can solve experimental and observational problems
-- oscillations, dark matter and baryon asymmetry--
in the
MSM
21 Sept. 2005 24
Conclusions
MSM