1. STERILE NEUTRINOS and other exotica

2. Neutrino physics Official do-it list  13 ? Improve  12,  23 Mass hierarchy Improve m 1, m 2, m 3 Dirac or Majorana CP violation astronomy

3. 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 =-M D (1/M I )(M D ) T –Majorana mass M I –Dirac mass M D =fv v=174 GeV vac exp val of Higgs field Usual choice: f as in quark sector, M = 10 10 -10 15 GeV Alternative choice: small f Inputs: m( 1 )= 10 -5 eV, m( 2 )= 9 meV, m( 3 )= 50 meV and mixings

4. Three sterile neutrinos Three singlet RH neutrinos N 1 N 2 N 3  N 1 with very large lifetime, Best choice : m(N 1 )  10 keV  N 2, N 3 almost degenerate (leptogenesis) With masses 100 MeV-few GeV

5. Decay of a 10 keV neutrino N 1  3, but also radiative decay Almost stable  DARK MATTER  Warm dark matter

6. Limits from cosmology Search for N 1 radiative decays Big Bang nucleosynthesis limits for N 2, N 3 U 2 < 10 -8 (1/m(GeV)) 2

7. Heavy neutrinos at accelerators Mixed with active neutrinos In all weak decays they appear at the level U 2 Nl Their mass is limited by the parent particles   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

8. Change in kinematics K  eNK   N Helicity conservation revisited

9. Decays of heavy neutrinos Purely weak decays: modes depend on the N mass first open channel e + e -, then  e,  +  -, e -  +,  -  + …. Lifetime for e + e -  2.8 10 4 (1/m(MeV) 5 )(1/U 2 )

10. PS191 experiment (1984!) 5 10 18 pots 19 GeV

11. « Typical » event

12. PRESENT LIMITS

13. Mixing to the  With the NOMAD experiment, 450 GeV p Source D s   

14. MiniBoone excess ? About 100 events depositing 300-400 MeV energy Obtained with 5 10 20 pots of 8 GeV

15. Possible interpretation Theoretical prejudice in the frame of MSM model: Decay of the N 2 component mixing predominantly to  (testing U N  2 ) 130 MeV < m < 350 MeV

16. Guesstimates N produced in Kaon decays  Flux 3 10 16 U 2 Corrections due to kinematics x 3 And also from focalisation x 5 Decay probability :  c  (m) = 10 13 E(MeV)/m 6 U 2 m = 150 MeV U 2 = 10 -7 m = 200 MeV U 2 = 4 10 -8 m = 250 MeV U 2 = 2 10 -8 NOT EXCLUDED !!

17. Improving on PS191 Modern beam: NuMI (25 years later) 120 GeV, 16 10 20 pots –Large , K production –  improvement in U 2 limits –Furthermore, with D production mass range can be extended to 1.3 GeV

18. NuMI beam neutrino flux on the MINERvA detector

21. (Parenthesis on the LHC) LHCb 10 12 B mesons/year of 100 GeV/c Mass region extended to 4 GeV ATLAS/CMS 3 10 8 W/year Mass region extended to 50 GeV

22. U 2 10 -6 10 -7 10 -8 10 -9 10 -10 0 0.1 0.2 0.3 0.4 GeV 0 0.5 1.0 GeV 0 10 20 30 40 GeV Miner a Rough expectations K±K± D±D± LHC B W±W±

23. E.M. interactions of neutrinos 1)Magnetic moment 2)Radiative decays 3)Stimulated conversion 2 1 W  l

24. Radiative decays Theory: GIM suppressed  = 7 10 43 1/m 5 1/U 2 (s) Experiment: 1) Mass hierarchy E  = E /2 SN anti- e  /m > 6 10 15 s/eV Los Alamos   /m > 15,4 s/eV 2) Degenerated masses E  = E  m 2 /m 2 = 2 E  m/m Bugey anti- e  /m > 2 10 -4 s/eV if  m/m > 10 -7 Solar eclipse   /m > 100 s/eV if  m 2 ~ 10 -5 eV 2

25. Matter enhancement Coherent interactions on atomic electrons e 2 W 1  e  0 /  m ~ 3 10 24 (N e /10 24 ) 2 (m/E) (1eV/m) 4

26. dE/dx by neutrinos We exposed a HP Ge crystal (140 cm 3 ) to a beam - First, in the HE (24 GeV) CERN beam Continuous current increase above leakage current during spills (4 pA) proportional to the beam intensity < 10 -5 eV/cm for  (10 -12 of mip) < 10 -3 eV/cm for e This translates into radiative lifetime limits  /m > 10 -16 E  s/eV for 5 10 -11 <  m/m < 2 10 -8 In vacuum equivalent to  0 > 10 19 /E  /m 2 (s)

27. dE/dx by neutrinos, cont. Then, at the Bugey reactor 1 hour exposure, beam off! e beam ( e /anti- e = 2 10 -4 from 55 Fe and 51 Cr) Looking for e  ’ +  (explanation of solar deficit) Result:  /m > 3 10 -4 s/eV Equivalent to:  0 > 9 10 15 s

28. Stimulated conversion in RF cavity Another possibility to overcome GIM suppression M.C Gonzalès-Garcia, F. Vannucci and J. Castromonte Phys.Lett. B373,153(1996) Idea: RF cavity is a bath of photons (10 26  of 10 -6 eV) On-off method Majorana neutrinos   anti- e or anti-  Dirac neutrinos   sterile R =  N/N = (Q/10 9 )(P/100W)(m/eV) 3 (eV 2 /  m 2 ) 3 (s/  )  0 = 20/R (m/  m 2 ) 3 If R 4 10 15 s for  m 2 = 8 10 -5 eV 2 and m = 1 eV If a signal were to be found, possibility to measure absolute masses and CP effects

29. Conclusion Sterile neutrinos: The MSM is an appealing model It is possible to test it simply in the NuMI beam and beyond. EM interactions of neutrinos: Large improvements possible, with a very small effort.