8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 1/12

The ν MSM, Dark Matter and

Neutrino Masses

Mikhail Shaposhnikov

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 2/12

Outlin

The ν MSM

Dark matter

Active neutrino masses

Conclusions

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 3/12

The ν MSM

Simplest extensions of the Standard Model incorporating neutrino

masses (four-dimensional renormalizable field theory)

Higgs sector: add new SU(2) Higgs triplets with small VeV: no

new fermionic degrees of freedom. Besides ν oscillations, noother physical output...

Fermionic sector: add singlet right-handed neutrinos

N D + N C + N B : the ν MSM. Can explain also dark matter and

baryon asymmetry of the Universe!

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 4/12

Lagrangian of ν MSM.

Most general renormalizable Lagrangian

LνMSM = LMSM + N I i∂ µγ µN I − F αI LαN I Φ −M I

2N cI N I + h.c.,

Extra coupling constants:

3 Majorana masses of new neutral fermions N i,

15 new Yukawa couplings in the leptonic sector

(3 Dirac neutrino masses, 6 mixing angles and 6 CP-violating phases),

18 new parameters in total. The number of parameters is doubled in compari-

son with the MSM.

Compare with MSSM: ∼ 100 new degrees of freedom, ∼ 100 newparameters...

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 5/12

The scales of ν MSM

Assume:

all mass scales are < M W ∼ 100 GeV

the Dirac neutrino masses ∼ F v M M are smaller than

Majorana masses

Then see-saw formula works:

M ν = −M D 1M M

M T D .

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 6/12

DM candidate: the lightest Majorana ν

Dodelson, Widrow, Shi, Fuller, Dolgov, Hansen, ...

Yukawa couplings are small →

sterile N can be very stable.

N

ν ν

ν

Z

Main decay mode: N → 3ν .

For one flavour:

τ N 1 = 5×1026

sec1keV

M 15 10−8

Θ2

Θ =mD

M M

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 7/12

Cosmological production of sterile neutrinos

Dodelson, Widrow, Dolgov, Hansen, Abazajian, Fuller, Patel

If Yukawa coupling is very small, sterile neutrino never equilibrates,

ΩN h2 ∼ 0.1

I

α=e,µ,τ |ΘαI |2

10−8 M I

1 keV2

.

Production temperature ∼ 130

M I

1 keV1/3

MeV.

Extreme complication - exactly the point where the quark-gluon plasma

is strongly coupled and the dilute hadron gas picture is not valid!

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 8/12

Consequences of dark matter sterile neutrino

Abazajian, Fuller, Tucker

Astrophysics: radiative decays

N → γν can be detected.

Chandra, XMM-Newton, and

future Constellation X observa-

tories.

Present upper limit:

M 1 < 5 KeV.

N

ν

e

W

γ

N

ν

W

e

γ

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 9/12

Structure formation and warm dark matter

M. Viel, J. Lesgourgues, M. G. Haehnelt, S. Matarrese and A. Riotto

Sterile neutrino: Warm Dark Matter (WDM) particle with large free

streaming length.

The matter power spectrum at comoving scales of (1− 40)h−1

Mpc issensitive to M 1.

WMAP (cosmic microwave background) and the matter power

spectrum inferred from Lyman-α forest data: M 1 > 2 KeV.Conclusion: only small window is allowed,

2 keV < M 1 < 5 keV

Taup 2005, Zaragoza, September 11, 2005 – p.

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 10/12

Active neutrino masses

Asaka, Blanchet, MS

Particle physics: The minimal number of sterile neutrinos, which can

explain the dark matter in the universe, is N = 3. Only one sterile

neutrino can be the dark matter.

Absolute values of the active neutrino masses:

m1 ≤ mdmν = O(10−5) eV.

Normal hierarchy:

m2 = [9.05+0.2−0.1] · 10−3eV ∆m2

solar ,

m3 = [4.8+0.6−0.5] · 10−2eV

∆m2

atm ,

Inverted hierarchy: m2,3 = [4.7+0.6−0.5] · 10−2 eV .

Taup 2005, Zaragoza, September 11, 2005 – p.1

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 11/12

Outline of the proof, one generation

Production of N goes through the processes like:

ν

Z

e

e

Ν

F ν

+

_

From production :

I

α=e,µ,τ

M DIα

2

= m20

, m0 = O(0.1)eV

Asaka, Blanchet, MS

From see-saw formula: mν m2

0

M I< 10−5 eV

Many generations: linear algebra and computation of determinants.Taup 2005, Zaragoza, September 11, 2005 – p.1

8/3/2019 Mikhail Shaposhnikov- The nu-MSM, Dark Matter and Neutrino Masses

http://slidepdf.com/reader/full/mikhail-shaposhnikov-the-nu-msm-dark-matter-and-neutrino-masses 12/12

Conclusions

The physics at the electroweak scale can explain simultaneously

neutrino oscillations

dark matter

baryon asymmetry of the universe

Predictions:

active neutrino masses

specific range of sterile neutrino masses

Dark matter is warm and not cold

Gamma-flux from DM

Taup 2005, Zaragoza, September 11, 2005 – p.1