1. Neutrino Oscillation and CPT Violation Hitoshi Murayama Caltech April 12, 2002

2. 2 Puzzle with Beta Spectrum Three-types of radioactivity:  Both  discrete spectrum because E   = E i – E f But  spectrum continuous F. A. Scott, Phys. Rev. 48, 391 (1935) Bohr: At the present stage of atomic theory, however, we may say that we have no argument, either empirical or theoretical, for upholding the energy principle in the case of  -ray disintegrations

3. 3 Desperate Idea of Pauli

4. 4 Three Kinds of Neutrinos There are three And no more

5. 5 Very strong evidence for neutrino oscillation from atmospheric and solar neutrinos What about LSND?

6. 6 Outline LSND LSND and SN1987A Sterile Neutrinos CPT Violation Models of CPT Violation Implications on Experiments Conclusions

7. 7 LSND

8. 8

9. 9 3.3  Signal Excess positron events over calculated BG

10. 10 Neutrino mode They also studied DIF (decay in flight) negative muons Claimed signal in  to e at ~2 sigma level Final analysis reduced the significance. Not even mentioned any more.

11. 11 Mini-BooNE LSND unconfirmed Neutrino beam from Fermilab booster Settles the issue of LSND evidence Start data taking later this year

12. LSND and SN1987A

13. 13 Kamiokande-II SN1987A in Large Magellanic Cloud ~150,000 light years away Burst of neutrino events at Kamiokande-II and IMB

14. 14 SN1987A Neutrino Burst

15. 15 SN1987A Neutrino Burst

16. 16 SN1987A neutrino burst doesn’t like LSND HM, Yanagida Kamiokande’s 11 events: –1st event is forward may well be e from deleptonization burst (p e -  n e to become neutron star) –Later events most likely e because its cross section of inverse beta decay is much larger than elastic scattering for other neutrino species LSND parameters cause complete MSW conversion of e   if light side ( e lighter) e   if dark side ( e heavier) Either mass spectrum disfavored _ __

17. 17 The Light side e   if light side ( e lighter) –You will lose the precious first event from neutronization burst into  –Of course, based on one event, you can’t say it strongly, though. The weakest argument in this talk.

18. 18 The Dark Side e   if dark side ( e heavier) –Temperature hierarchy from supernova –T( e )~10–12MeV –T( e )~14–17MeV – T(         )~24–27MeV Observed at Kamiokande-II –T( e )~7–14MeV If complete conversion, the events must be much hotter _ _ __

19. 19 Nuclear r-process For the neutrino-driven wind in the supernova envelope to be the site for nuclear r-process, you want it to be neutron-rich Enemy: n e  p e – to lose neutrons If e hotter due to conversion from   you would lose more neutrons and destroy the r-process (Qian-Fuller)

20. 20 SN1987A neutrino burst doesn’t like LSND HM, Yanagida P osc <90% P osc <35%

21. Sterile Neutrinos

22. 22 Sterile Neutrino LSND, atmospheric and solar neutrino oscillation signals  m 2 LSND ~ eV 2  m 2 atm ~ 3  10 –3 eV 2  m 2 solar < 10 –3 eV 2   Can’t be accommodated with 3 neutrinos   Need a sterile neutrino New type of neutrino with no weak interaction 3+1 or 2+2 spectrum?

23. 23 Sterile Neutrino getting tight 3+1 spectrum: sin 2 2  LSND =4|U 4e | 2 |U 4  | 2 –|U 4  | 2 can’t be big because of CDHS, SK U/D –|U 4e | 2 can’t be big because of Bugey –Marginally allowed (90% excl. vs 99% allw’d) –(Barger et al, Giunti et al, Gonzalez-Garcia et al, Strumia)

24. 24 3+1 spectrum Strumia

25. 25 Sterile Neutrino getting tight 2+2 spectrum: past fits preferred –Atmospheric mostly    –Solar mostly e  s (or vice versa) –Now solar sterile getting tight (Barger et al, Giunti et al, Gonzalez- Garcia et al, Strumia)

26. 26

27. 27

28. 28 Josh Klein, Lepton Photon 2001

29. 29 SNO SNO: e SuperK: e +  /7 3.3  difference   are coming from the Sun!

30. 30 SNO result Total 8B flux: (5.44  0.99)  10 -9 cm -2 s -1 BP2000 calculation (5.05 +0.1 -0.8 )  10 -9 cm -2 s -1 Remarkable agreement! Not much room for sterile neutrinos

31. 31 Wrong Neutrinos Only e produced in the Sun Wrong Neutrinos   are coming from the Sun! Somehow some of e were converted to  on their way from the Sun’s core to the detector  neutrino oscillation! SNO is further studying neutral current reaction   e +  +  Expect result in April!

32. 32 2+2 Spectrum also disfavored Global fit to four- neutrino oscillation –Solar, Atmospheric, LSND (Gonzalez-Garcia, Maltoni, Peña- Garay@EPS01) One can look for a compromise solution with 2+2 spectrum  Disfavored at 90-99% CL e  s    e     s

33. CPT Violation

34. 34 CPT Violation? “A desperate remedy…” LSND evidence: anti-neutrinos Solar evidence: neutrinos If neutrinos and anti- neutrinos have different mass spectra, atmos- pheric, solar, LSND accommodated without a sterile neutrino (HM, Yanagida)

35. 35 CPT violation in atmospheric neutrinos CPT violation not needed, but allowed (Strumia) Anti-neutrino mass- squared less constrained because of lower event rates

36. 36 Best Global Fit CPT violation provides much better fit to solar, atmospheric, LSND, and other limits (Strumia)

37. 37 Is it allowed??? We need CPT violation in neutrino mass of ~0.1– 1eV Neutral kaon mass limit But, consider mass-squared as a natural parameter: LSND mass range compatible

38. 38 CPT Theorem Based on three assumptions: –Locality –Lorentz invariance –Hermiticity of Hamiltonian Violation of any one of them: big impact on fundamental physics Neutrino mass: tiny effect from high-scale physics –Non-commutative geometry? (HM, Yanagida) –Brane world? (Barenboim, Borissov, Lykken, Smirnov)

39. Models of CPT Violation

40. 40 Trivial Idea If you write down the Hamiltonian in momentum space, it is easy to break CPT Still Lorentz invariant, but cannot be written in terms of a local field.

41. 41 Extra Dimensions Right-handed neutrinos SM gauge singlet Can propagate in the “bulk” Makes neutrino mass small (Arkani-Hamed, Dimopoulos, Dvali, March-Russell; Dienes, Dudas, Gherghetta; Grossman, Neubert) m ~ 1/R if one extra dim  R~10  m An infinite tower of sterile neutrinos Need also inter-generational mixing now

42. 42 CPT Violation in the Bulk Write down CPT-violating Hamiltonian for the right-handed neutrinos in the bulk The only particle on the brane that picks up that effect would be neutrinos through the mass terms. CPT-violation appears only in the neutrino mass (Barenboim, Borissov, Lykken Smirnov)

43. 43 Dipole Field Theory Start with a standard quantum field theory Make it non-local by introducing a “dipole vector” L to every field Product of fields is defined by Can be obtained as a limit of string theory (Bergman, Dasgupta, Ganor, Karczmarek, Rajesh) Non-local Lorentz- violating theory Dipole vector L changes sign for conjugate field But electric dipole moment CPT-even CPT violation! (Ganor; private communication)

44. Implications on Experiments

45. 45 Mini-BooNE Plans to run in neutrino mode If CPT violated, won’t neither refute nor confirm LSND They can run in anti- neutrinos Lower rate requires twice as much running time

46. 46 KamLAND Reactor anti-neutrino experiment KamLAND will exclude or verify LMA definitively But if CPT violated, KamLAND won’t confirm neutrino oscillation

47. 47 KamLAND If KamLAND sees LMA, it excludes CPT violation of this particular type If KamLAND doesn’t see LMA, it may still be LMA together with CPT violation LMA then needs to be established by exclusion

48. 48 Day/Night Effect in CC @ SNO

49. 49 VAC by seasonal variation 7 Be neutrino monochromatic seasonal effect probes VAC region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

50. 50 VAC by seasonal variation Fit to seasonal variation to measure parameters Can pep resolve degeneracy?

51. 51 LOW by day/night effect 7 Be neutrino monochromatic Day/night effect probes LOW region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

52. 52 LOW by zenith angle dependence More information in zenith angle depend. (de Gouvêa, Friedland, HM)

53. 53 SMA by pp neutrinos SMA: Sharp falloff in probability in the pp neutrino region the survival Because of the condition for the level crossing Measure the falloff   m 2 measurement

54. 54 Can pp neutrinos be studied? CC+NC (electron recoil) –gaseous He TPC –HERON: superfluid He (phonon & roton) –liquid Xe –GENIUS: Ge CC ( e capture) –LENS: Yb or In –MOON: Mo LENS-Yb

55. 55 By exclusion… If none of these attempts succeed, solar neutrinos must be LMA by exclusion Negative signal at KamLAND then implies CPT violation

56. 56 Lepton-number Violation? Neutrino Hamiltonian analogou to neutral kaons: m: CPT-conservating mass  : CPT-violating mass y: lepton-number violating mass

57. 57 0  LSND mass scale 0.1–1eV is interesting from the point of view of neutrinoless double beta decay If CPT violated, LSND mass scale may show up in the neutrinoless double beta decay 0<m  <0.1m LSND (Barenboim, Beacom, Borissov, Kayser)

58. 58 Conclusions If all data and indications taken literally, CPT violation the most preferred explanation to data Of course, it is a highly exotic possibility But after all, we are interested in neutrinos because they tell may us something about extremely rare phenomena from very-high- energy physics

59. 59 Maybe even more surprises in neutrinos!