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