Answers to some of the questions

1. Answers to some of the questions Q1. Where do the following relation come from? A1. In the standard model, the couplings of are,  suekane@FAPPS

2. Q2. You said and are different particle from the Davis's negative result at reactor. But if neutrino is Majorana, they can be same. A1. Yes. It is exactly the introductory discussion about the 0n2b experiment. To explain this, I will borrow next 3 slides from tomorrows lecture. What I meant yesterday were that at that time of the experiment, before the idea of Majorana particle, the experimental result could be understood so. suekane@FAPPS

3. from tomorrows slide -1 e- e- ν π- n So far neutrino and anti-neutrino are considered to be different particle because e- e+ ν This takes place. π+ n But not this. So that 2005.1.13 non-accel. F.Suekane suekane@FAPPS 3

4. from tomorrows slide -2 Chirality Conservation vL vR uL uL g/W/Z/G g/W/Z/G For EM, Weak and Strong interactions, the final chiralirty is always same as initial chirality suekane@FAPPS

5. from tomorrows slide -3 e- ν e+ e- π+ n e- ν π- n Another possibility Chirarity conserves The neutrino produced with positron has positive chirarity and can not produce negative chirarity electron through weak interaction. Chirarity changes So that n and are not necessarily different particle suekane@FAPPS

6. Q The point of of yesterday's lecture a a b b a b Whatever the a, b are, the time dependent general state is P R q R-P where, q is defined in the right figure; and suekane@FAPPS

7. The point of of yesterday's lecture If initial condition is pure state, , C1=cos(q/2), C2=-sin(q/2) and the wave function at later time t is, Then the probability we observe state is If a, b are neutrino flavor state; ne, nm, it is called neutrino oscillation. If they are spin under magnetic field, it is called spin precession. suekane@FAPPS

8. The point of of yesterday's lecture If we choose, C1=1, C2=0, we get an energy eigenstate If we choose, C1=0, C2=1, we get another energy eigenstate The relation between the energy eigenstates and the state a,b is q/2 is called mixing angle. That's all. suekane@FAPPS

9. d' s' Answer to another very good question Q3, What is the "magnetic field" of n oscillation? d' d' A3, We do not know. It is the very physics we study by n oscillation (and mass). For the case of quarks (quarks oscillate as well) there are transition amplitudes (T.A.); s' s' Q P R The quark masses are generated from the T.A. suekane@FAPPS

10. We understand the quark masses are generated from the coupling to the Higgs potential. => The "magnetic field" of the quark T.A. is the Higgs field. We may think the "magnetic filed" of n flavor transition is the Higgs field as well. However the coupling constant (mn) is very small compared with quark's (mq) and theorists do not like it. Theorists believes there should be other mechanism to generate n T.A., such as the see-saw mechanism, which naturally explains smallness of mn, while keeping n T.A. similar size of quark's. To study these kinds of things is an ultimate purpose of current neutrino physics. To do so, experimentalists' mission is to measure the T.A.'s, to check if , to measure imaginary component of T.A. (CP violation), etc. ... And theorists' mission is to explain them and explain our world using the information. (I am happy the analogy of spin worked very well so as to lead this explanation) suekane@FAPPS

11.  e e 2 mmee Back tothe Oscillation: n at rest We assume there are transition amplitudes between ne and nm R e e P Q   mee m Caution!! from now on we define the angle q as just for convention of neutrino oscillation people suekane@FAPPS

12.  e e 2 mmee Oscillations: n at rest e e   Then the energy eigenstates and their energy can be obtained borrowing spin result mee m suekane@FAPPS

13. Mass of ne This title sounds to be a paradoxical since ne is not mass eigenstate and does not have fixed mass; But this wve function means if we measure ne mass, m- is observed with probability cos2q andm+ is observed with probability sin2q. If the experiment does not have enough accuracy to separate m+ and m– (and this is always so if we know we measure ne property) what we observe is the average of them. Energy resolution # of events sin2q cos2q m- m+ What we observe by experiment suekane@FAPPS

14.  e e Relation between average ne mass and T.A. And likewise e e In that sense, we can call the transition amplitudes mee (mmm) as "electron (muon) neutrino mass", respectively.     mee m e e  e If you like, you may re-write. e suekane@FAPPS

15. Oscillation of relativistic n Usually text books explain it starting from Then because, And finally get the standard formula But why we can say p is same? What is the E in the final formula? This delivation is based on plain waves. It it OK? suekane@FAPPS

16. Oscillation of relativistic n Actually the formalism of oscillation of relativistic neutrino is not easy. A prominent theorist said, There are still some discussions about the theory of neutrino oscillations even in vacuum. .. The issues become important.. where the uncertainty in energy is much smaller than the oscillation frequency. byA.Y.Smirnov@Neutrino2008, Arxive/hep-ph0810.2668 Even nowadays sometimes I see preprints discussing this issue on arXive. So probably most of us do not understand it yet. But experimentalists know neutrino is oscillating by heart from their data. So I would like to push theorists to let us understand it! suekane@FAPPS

17. Oscillation of relativistic n Because most of us do not understand it, it may be allowed to think of it as following way. It makes an issue of n oscillation experiment clear. If neutrino oscillation at rest is seen from the system which moves with velocity –b with respect to the system, from Lorentz transformation, n-Oscillation at rest where, Lorenz factor: suekane@FAPPS

18. Oscillation of relativistic n From this system the neutrino energy looks as, => Since we do not know the absolute n masses, we do not know Lorentz factor g even if we know the energy. This introduces additional uncertainty when extracting T.A. from the data. (It is not the case for K0 oscillation and quark oscillation.) (It should be OK to use g=E-/m- and use as well.) suekane@FAPPS

19. e e   mee m  e e 2 mmee What We Measure by n Oscillation? Relation between observable and T.A. Both mass and mixing are combinations of flavor transition amplitudes. • Measurement of mixing angle is as important as measurement of mass. suekane@FAPPS

20. If we could measure Dm2, q, and all the transition amplitude can be determines. suekane@FAPPS

21. Purpose of  Oscillation experiments Physics of  oscillation is to measure the flavor transition amplitudes and think of its origin   Now we know exists. H0 H0 Non Standard Higgs? or ? Sub Structure?? PS mixing G d s d s For Example, Or something else?? ? suekane@FAPPS

22. n Oscillation Experiments so far Atmospheric n * SuperKamiokande * MACRO * Soudan-2 Accelerator n * LSND * K2K * T2K * MINIBOONE * MINOS * OPERA Solar n * Homestake * SAGE * GALLEX/GNO * SuperKamiokande * SNO Reacotor n * Chooz * Paloverde * KamLAND suekane@FAPPS

23. Murayama 2 oscillations measured m2~2.6x10-3eV2, sin22~1.0 Atmospheric Accelerator How they were measured? 1 upper limit measured Solar Reactor sin22<0.13 @m2=2.6x10-3eV2 m2~7.6x10-5eV2, sin22~0.87 suekane@FAPPS

24. Atmospheric n nm nm ne suekane@FAPPS

25. Atmospheric n anomaly Expected. neutrino Observation => R<2 ?? Atmospheric n anomaly. L Detect n from the other side of the Earth. L=2Rcosq => L dependence of atmospheric n disappearance. Earth q detector suekane@FAPPS

26. Atmospheric n experiments Soudan Macro suekane@FAPPS

27. Kajita Nufact04 SI 1997: 1st Discovery of neutrino oscillation by atmospheric neutrinos suekane@FAPPS

28. Detection of Atmospheric n by water cherenkov detector Water m Clear Cherenkov ring e EM shower e Blurred Cherenkov ring Water suekane@FAPPS

29. Kajita, Nufact04 SI suekane@FAPPS 29 29

30. 1998 3588 cites (as of 15/Sep/2011) (1)Deficit of nm (2) ne as expected =nmnt Oscillation ne (2) (1) sin22q~1 Dm2~2x10-3eV2 nm suekane@FAPPS

31. Kajita Fufact04 Recovery of event rate in L only occurs by oscillation. Not by one-way processes like decay and decoherence 2004 suekane@FAPPS

32. Kajita Fufact04 suekane@FAPPS

33. Kajita, Nufact04 SI Long Baseline Accelerator Experiments (=high energynm beam) MINOS K2K/T2K (NOVA) OPERA suekane@FAPPS

34. K2K=KEK to Kamioka K2K ~2004 suekane@FAPPS

35. tjampens Nufact04 suekane@FAPPS

36. How n beam is generated (Helicity Suppression => Almost pure nm Main ne contamination comes from suekane@FAPPS

37. Synchronization of timing =Removal of Backgrounds suekane@FAPPS

38. K2K result suekane@FAPPS

39. suekane@FAPPS

40. MINOS oscillation measurement suekane@FAPPS

41. MINOS oscillation measurement Change the polarity of the magnets in the beam line D.Naples@TAUP2011 CPT is OK suekane@FAPPS

42. suekane@FAPPS

43. OPERA * Appearance of * nt+X t+X' and identify t by nuclear emulsion hybrid detector. * Maybe the 1st experiment to confirm appearance. (So far all the n oscillation experiments measured disappearance) * Difficulty are that the mt is large and difficult to produce t (En>3.5GeV) and that t is difficult to identify. It decays to m or e within 1mm and difficult to separate from nm+X m+X' unless decay vertex is identified. suekane@FAPPS

44. suekane@FAPPS

45. suekane@FAPPS

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47. This is more famousnow for OPERA It is a great discovery if it is true. But needs independent tests. suekane@FAPPS

48. Summary of atom. & LBL accel. n experiments Atmospheric K2K K2K(positive) MINOS T2K suekane@FAPPS

49. Solar n (=low energy ne) Production of solar n n flux @ Earth suekane@FAPPS

50. Solar neutrino spectrum suekane@FAPPS