STERILE NEUTRINOSand

WARM DARK MATTER

The MSM model• T. Asaka and M. Shaposhnikov Phys.Lett.B620(2005)17• M.Shaposhnokov Nucl.Phys.B763(2007)49

• Minimum extension of the SM to accomodate massive neutrinos

• See-saw formula for active neutrinos m=-MD(1/MI)(MD)T

– Majorana mass MI – Dirac mass MD=fv v=174 GeV vac exp val of Higgs field

• Usual choice: f as in quark sector, M = 1010-1015 GeV

• Alternative choice: small f

Ne, N, N

A simple calculationIn the Universe at large:

Dark matter 25%Ordinary matter(nucleons) 5%Nucleon/photon = 6 10-10

400 /cm3, 100 e/ cm3

Putting all the numbers togetherIn the Universe at largeN/ = 3.6 10-6/m

(m in MeV)

Thus : N/e = 1.2 10-5/m

UNe2 > 1.2 10-5/m

Testing the anomalies

Reactor and rad source anomaly 1.2 10-5/m = 7%

m = 180 eV !!

LSND anomaly 1.2 10-5/m = 1%

m = 1.2 keV

N as Dark Matter Candidate

Suppose that DM is made of heavy neutrinos of mass m MeV Density of DM 300 MeV/cm3

Number density of N 300/m /cm3

Relative velocity 200 km/s Flux 6109/m /cm2/s

But the earth moves at 30 km/sYearly modulation

In December 5,1 109/m /cm2/sIn June 6,9 109/m /cm2/s

Possible experiments?

Decay of sterile neutrinos If mass < 1 MeV

If mass > 1 MeVPurely weak decay: Lifetime for e+e-

2.8 104 (1/m(MeV)5)(1/U2)(s)

+ phase-space

W

e

Radiative decay: GIM suppressed = 7 1013 (1/m(MeV)5)(1/U2)(s)

Weak/radiative ~ 1010

Heavy neutrinos at accelerators

• Mixed with active neutrinos

• In all weak processes they appear at the level U2Nl

Their mass is limited by kinematics

e N m(N) < 130 MeV

N m(N) < 20 MeV

K e N m(N) < 450 MeV

K N m(N) < 350 MeV

… W e N m(N) < 80 GeV

PRESENT LIMITS

Consistancy problemUNe

2 > 1.2 10-5/m ??

Livetime must be greater than the age of the Universe

For N → e+ e-

2.8 104 (1/m(MeV)5)(1/U2)→ m<10keV !

For N → = 7 1013 (1/m(MeV)5)(1/U2)

→m<1.5 MeV

Astrophysics searches

A.Boyarsky, D.Malyshev, A.Neronov, O.Ruchaysky arXiv:0710.4922H.J.de Vega, N.G.Sanchez Mon.Not.R.Astron.Soc.(2010)

From SPI (Integral) and XMM-Newton

Laboratory search?Flux 61012/m(keV) /cm2/s

Radiative decay = 7 1028 (1/m(keV)5)(1/U2)(s)

But matter enhancement

e

W

e

0/m ~ 3 1012 (Ne/1024)2 (m/E) (keV/m)4

m ~ 2 1016 (keV/m)(1/U2)

Probability of decay is l/(c) = 0,7 10-3, = 1

In 1 m3 detector N = 1.3 U2 events/day

Interactions of keV sterile neutrinos: S.Ando, A.Kusenko arXiv:1001.5273

Conclusion

• Heavy neutrinos probably exist• Potentially predicting Warm Dark Matter

(… but problematic consistancy)

• Experimentally extremelly challenging