1. STERILE NEUTRINOS and WARM DARK MATTER

2. The nMSM 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 mn=-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 = GeV
Alternative choice: small f
 Ne, Nm, Nt

3. A simple calculation In the Universe at large: Dark matter 25%
Ordinary matter(nucleons) 5%
Nucleon/photon =
400 g/cm3, 100 ne/ cm3
Putting all the numbers together
In the Universe at large
N/g = /m
(m in MeV)
Thus : N/ne = /m
UNe2 > /m

4. Testing the anomalies Reactor and rad source anomaly 1.2 10-5/m = 7%
m = 180 eV !!
LSND anomaly
/m = 1%
m = 1.2 keV

5. N as Dark Matter Candidate
Suppose that DM is made of heavy neutrinos of mass m MeV Density of DM MeV/cm3
Number density of N 300/m /cm3
Relative velocity km/s
Flux /m /cm2/s
But the earth moves at 30 km/s
Yearly modulation
In December 5,1 109/m /cm2/s
In June ,9 109/m /cm2/s
Possible experiments?

6. Decay of sterile neutrinos
 If mass < 1 MeV W
Radiative decay: GIM suppressed
t = (1/m(MeV)5)(1/U2)(s) N n e g
 If mass > 1 MeV
Purely weak decay: Lifetime for e+e-n
t = (1/m(MeV)5)(1/U2)(s)
+ phase-space
Weak/radiative ~ 1010

7. Heavy neutrinos at accelerators
Mixed with active neutrinos
In all weak processes they appear at the level U2Nl
Their mass is limited by kinematics
p  e N m(N) < 130 MeV
p  m N m(N) < 20 MeV
K  e N m(N) < 450 MeV
K  m N m(N) < 350 MeV
… W  e N m(N) < 80 GeV

8. PRESENT LIMITS

9. Consistancy problem UNe2 > 1.2 10-5/m ??
Livetime must be greater than the age of the Universe
For N → n e+ e-
t = (1/m(MeV)5)(1/U2)
→ m<10keV !
For N → n g
= (1/m(MeV)5)(1/U2)
→m<1.5 MeV

10. Astrophysics searches
A.Boyarsky, D.Malyshev, A.Neronov, O.Ruchaysky arXiv:
H.J.de Vega, N.G.Sanchez Mon.Not.R.Astron.Soc.(2010)
From SPI (Integral) and XMM-Newton

11. Laboratory search? Flux 61012/m(keV) /cm2/s
Probability of decay is l/(bgct) b = 0,7 10-3, g = 1
Radiative decay
t = (1/m(keV)5)(1/U2)(s) N g
But matter enhancement e W e n
t0/tm ~ (Ne/1024)2 (m/E) (keV/m)4
tm ~ (keV/m)(1/U2)
In 1 m3 detector N = 1.3 U2 events/day
Interactions of keV sterile neutrinos: S.Ando, A.Kusenko arXiv:

12. Conclusion Heavy neutrinos probably exist
Potentially predicting Warm Dark Matter
(… but problematic consistancy)
Experimentally extremelly challenging