STERILE NEUTRINOS and WARM DARK MATTER

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 = 1010-1015 GeV Alternative choice: small f  Ne, Nm, Nt

A simple calculation In the Universe at large: Dark matter 25% Ordinary matter(nucleons) 5% Nucleon/photon = 6 10-10 400 g/cm3, 100 ne/ cm3 Putting all the numbers together In the Universe at large N/g = 3.6 10-6/m (m in MeV) Thus : N/ne = 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/s Yearly modulation In December 5,1 109/m /cm2/s In June 6,9 109/m /cm2/s Possible experiments?

Decay of sterile neutrinos  If mass < 1 MeV W Radiative decay: GIM suppressed t = 7 1013 (1/m(MeV)5)(1/U2)(s) N n e g  If mass > 1 MeV Purely weak decay: Lifetime for e+e-n t = 2.8 104 (1/m(MeV)5)(1/U2)(s) + phase-space 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 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

PRESENT LIMITS

Consistancy problem UNe2 > 1.2 10-5/m ?? Livetime must be greater than the age of the Universe For N → n e+ e- t = 2.8 104 (1/m(MeV)5)(1/U2) → m<10keV ! For N → n g = 7 1013 (1/m(MeV)5)(1/U2) →m<1.5 MeV

Astrophysics searches A.Boyarsky, D.Malyshev, A.Neronov, O.Ruchaysky arXiv:0710.4922 H.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 Probability of decay is l/(bgct) b = 0,7 10-3, g = 1 Radiative decay t = 7 1028 (1/m(keV)5)(1/U2)(s) N g But matter enhancement e W e n t0/tm ~ 3 1012 (Ne/1024)2 (m/E) (keV/m)4 tm ~ 2 1016 (keV/m)(1/U2) 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