Neutrino Oscillation and CPT Violation

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

2. Three-types of radioactivity: a, b, g Both a, gdiscrete spectrum because Ea, g= Ei – Ef But b spectrum continuous F. A. Scott, Phys. Rev.48, 391 (1935) Puzzle with Beta Spectrum 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 b-ray disintegrations

3. Desperate Idea of Pauli

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

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

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

7. LSND

9. Excess positron events over calculated BG 3.3s Signal

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

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

12. LSND and SN1987A

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

14. SN1987A Neutrino Burst

15. SN1987A Neutrino Burst

16. SN1987A neutrino burstdoesn’t like LSND • Kamiokande’s 11 events: • 1st event is forward may well be ne from deleptonization burst (p e- n ne to become neutron star) • Later events most likely ne 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 nenm if light side (ne lighter) nenm if dark side (ne heavier) • Either mass spectrum disfavored _ _ _ HM, Yanagida

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

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

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 ne p e–to lose neutrons • If ne hotter due to conversion from nm ,you would lose more neutrons and destroy the r-process (Qian-Fuller)

20. SN1987A neutrino burstdoesn’t like LSND Posc<90% Posc<35% HM, Yanagida

21. Sterile Neutrinos

22. LSND, atmospheric and solar neutrino oscillation signals Dm2LSND ~ eV2 Dm2atm ~ 310–3eV2 Dm2solar < 10–3eV2  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? Sterile Neutrino

23. 3+1 spectrum: sin22qLSND=4|U4e|2|U4m|2 |U4m|2 can’t be big because of CDHS, SK U/D |U4e|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) Sterile Neutrino getting tight

24. 3+1 spectrum Strumia

25. 2+2 spectrum: past fits preferred Atmospheric mostly nmnt Solar mostly nens(or vice versa) Now solar sterile getting tight (Barger et al, Giunti et al, Gonzalez-Garcia et al, Strumia) Sterile Neutrino getting tight

28. Josh Klein, Lepton Photon 2001

29. SNO • SNO: ne • SuperK: ne+nm,t/7 3.3s difference nm,t are coming from the Sun!

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

31. Wrong Neutrinos • Only ne produced in the Sun • Wrong Neutrinosnm,t are coming from the Sun! • Somehow some of ne were converted to nm,t on their way from the Sun’s core to the detector  neutrino oscillation! SNO is further studying neutral current reaction  ne+nm+nt Expect result in April!

32. 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 2+2 Spectrum also disfavored ne nt nm ns nens nmnt

33. CPT Violation

34. 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) CPT Violation?“A desperate remedy…”

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

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

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. 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. 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. 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) • mn ~ 1/R if one extra dim  R~10mm • An infinite tower of sterile neutrinos • Need also inter-generational mixing now

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. 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) Dipole Field Theory

44. Implications on Experiments

45. 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 Mini-BooNE

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

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. Day/Night Effectin CC @ SNO

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

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