1. 1 Enrique Fernández Univ. Autónoma Barcelona/IFAE Neutrino oscillations: status and plans Trobada de Nadal, Univ. Barcelona, Dec 21-22, 2005

2. 2 Neutrino properties Neutrinos are somewhat special particles. This is mainly due to the fact that they only interact weakly. At low energies (MeV’s), the cross-section for interacting with 1 nucleon is very small, ~ 10 -40 cm 2. This implies that they are “invisible” in most cases. The charged current weak interaction is also very peculiar: it only acts on the left-handed chiral projection of particle spinors (right-handed, for antiparticles). It does not conserve P (nor CP). Spin effect are thus very strong. They also have a very small mass, compared with that of the other elementary particles.

3. 3 m u = 400m d = 400m e = 0.5m e < 0.0000022 m c = 1,600m s = 500m  = 106m  < 0.000170 m t =175,000m b =4,300m  = 1,776m  < 15.5 QuarksLeptones Quark and Lepton masses in units of MeV/c 2  m i <0.00000071 From CMB anisotropies: Neutrino properties

4. 4 Neutrinos in the SM In the SM there are 3 lepton families, each containing a charged lepton and a neutrino. Neutrinos are massless particles and each family lepton number (as well as global lepton number) is conserved. These assumptions, in particular the massless assumption, were built up from experiments. The neutrino has three states (weak eigenstates): e, ,   By definition these are the states that couple to the W together with the corresponding charged leptons.

5. 5 Massive neutrinos and neutrino oscillations In 1998 there was a turning point in neutrino physics. Data from atmospheric neutrinos collected by the Superkamiokande detector showed that there were neutrino oscillations. As we will see neutrino oscillations requires that neutrinos have mass and that there is lepton mixing. The SK results were preceded by many experiments on solar neutrinos that showed a deficit, with respect to solar models, on the number of neutrinos coming from the Sun. New solar neutrino experiments, in particular SNO (Sudbury Neutrino Observatory) have now shown unequivocally that the deficit of solar neutrinos is also due to oscillations.

6. 6 What do we mean by oscillations? (ref.: B. Kaiser, hep-ph/0506165). Let’s assume that a neutrino of flavor , , is produced at the source. When it interacts at the target it does so as a neutrino of a different flavor, .

7. 7 Oscillation requires both mixing between the leptons and massive neutrinos. Suppose that there are several neutrino mass states i. Mixing means that the state produced together with charged lepton l  is a superposition of different i : The set of all U *  i (for 3 i ) form a unitary matrix. Inverting it: Neutrino Oscillations: Pontecorvo-Maki-Nakagawa-Sakata matrix U *  i = amplitude of W + decay to l  i

8. 8 The oscillation probability is given by the square of the amplitude: Neutrino Oscillations:

9. 9 In the rest frame: In terms of laboratory variables: To interfere coherently, the different i have to have the same E. (if they had the same p the phase would be exp (-i(E i -E j )t) which, averaged over t, would be zero, unless E i =E j ). The momentum is given by (for m i 2 <<E 2 ): Therefore the phase is: (constant for all i, thus not contributing to the probability)

10. 10 Neutrino oscillations. Squaring the amplitude: The oscillation implies that lepton family number is no longer conserved.

11. 11 This is entirely similar to what happens in the case of the quarks, where favor is not conserved in weak decays, e.g  (uds)  p (uud)+   (du) The reason for the non-conservation of “quark family number” or “flavor” is quark mixing, the fact that weak and mass eigenstates are different. u d’ c s’ t b’ Neutrino Oscillations: The difference is that we produce weak-interaction quarks (in the weak decay of the  ) but observe them as mass states (in the p or  ).

12. 12 Neutrino oscillations. Squaring the amplitude: From this expression we see that: 1)as required by CPT invariance. 2)In general (if U complex):CP violation. The above formula is very complicated but nature has been kind enough as to make it simple in certain cases of interest. 3)The sin2[..L/E] gives “oscillatory” pattern.

13. 13 Neutrino oscillation: To gain some understanding of the above formula write: For a given term to be relevant the argument of sin 2 () should not be much smaller than  /2, otherwise sin 2 ( ) is too small. It can also be that for a given experiment only one mixing angle is relevant. The bottom line is that in some cases the oscillation can be treated as a two-family mixing.

14. 14 Neutrino oscillation: Oscillation probabilities (2 neutrino case; relevant for CNGS beam):

15. 15 The first clear signature of oscillations came from the SuperKamiokande experiment in 1998

16. 16 Detect Cherenkov light produced by charged lepton l  from reacction +N  l  +X ( l =e,  ), or e - from +e -  +e -. Detector operates in real time and has directional information. SuperKamiokande detector principle

17. 17 SuperKamiokande events (fairly typical) muonelectron

18. 18 Evidence for neutrino oscillations SK atmospheric

19. 19 Evidence for oscillatory signature in atmospheric neutrino oscillation (SK: PRL, 93, 101801 (2004)) L/E ~ 500 km/GeV 1.9x10 -3 eV 2 <  m 2 <3.0x10 -3 eV 2

20. 20 Events and MC for events after resolution cut:  (L/E) < 70%

21. 21 The evidence for oscillations: solar neutrinos All fusion reactions amount to: 4 p  4 He + 2e + + 2 e (Q=24.68 MeV) Assuming that  ’s and kinetic energy (except that of the ’s) go to heat, the heat production per reaction is W= Q+4m e c 2 - =26.1 MeV The total number of e ’s produced by the Sun is then: N = 2 L /W = 1.8x30 38 e. s -1 Flux on Earth surface = 6.4x10 10 e /cm 2 s -1 (day and night). One quantity that is easy to calculate is the total flux of neutrinos. This is because it can be related in a simple way to the total solar luminosity which is very well measured: L = 3.846 x10 26 watts

22. 22 The flux of solar neutrinos is very large but their detection is very difficult. The pioneer experiment of R.Davies took place at the Homestake Mine in S. Dakota (at 1350m depth). Large (600 tons) of Perchloroethylene (C 2 Cl 4 ). The detection method is radiochemical. The evidence for oscillations: solar neutrinos About 2 radioactive atoms/day!

23. 23 The evidence for oscillations: solar neutrinos The measurement was repeated by other experiments using Galium instead of Clorine. All of them saw less neutrinos than expected. This was known as the “solar neutrino problem”. Kamiokande, and later SK, measured the “elastic- scattering” reaction x + e - → x + e - where x is mostly e. e e  e e e-e- e-e- e-e- e-e- e-e- e-e- WZ Z

24. 24 The evidence for oscillations: solar neutrinos

25. 25 The evidence for oscillations: solar neutrinos

26. 26 Definive solution of the Solar neutrino puzzle The Sudbury Neutrino Observatory (SNO) SNO: 1 kT of D 2 O (heavy water) surrounded by 7.8kT of ultra pure H 2 O. Located at 2000m depth at the INCO mine in Sudbury, Ontario, Canada.

27. 27 Definive solution of the Solar neutrino puzzle A neutrino of E >2.2 MeV can disociate the Deuterium nucleous, into proton and neutron. This NC process takes place for any neutrino species. SNO SNO detects 3 reactions: e + D  p + p + e - (CC) x + e - → x + e - (ES; like SK) l + D  l + p + n (NC; l = e, ,  ) The neutron is captured producing 6.25 MeV. But detecting a single neutron is difficult... SNO detects 3 reactions: e + D  p + p + e - (CC) x + e - → x + e - (ES; like SK) l + D  l + p + n (NC; l = e, ,  ) The neutron is captured producing 6.25 MeV. But detecting a single neutron is difficult...

28. 28 Definive solution of the Solar neutrino puzzle SNO Results

29. 29 Oscillation signatures Atmospheric neutrino disappear, but, is it due to oscillations? A controlled accelerator experiment: K2K (KEK to Kamioka).

30. 30 K2K (KEK to Kamioka)  monitor  monitor Near detectors (ND) ++  Target+Horn 200m decay pipe SK 100m ~250km  12GeV protons ~10 11   /2.2sec (/10m  10m) ~10 6   /2.2sec (/40m  40m) ~1 event/2days  Signal of oscillation at K2K Reduction of  events Distortion of  energy spectrum (monitor the beam center) 1º tilt downwards

31. 31 SK Events (BG: 1.6 events within  500  s 2.4×10 -3 events in 1.5  s) T SK T spill GPS SK TOF=0.83msec 107 events Decay electron cut.  20MeV Deposited Energy No Activity in Outer Detector Event Vertex in Fiducial Volume More than 30MeV Deposited Energy Analysis Time Window  500  sec  5  sec T DIFF. (s) - 0.2  T SK - T spill - TOF  1.3  sec for 0.89x10 20 p.o.t.

32. 32 K2K near-detector complex 1KT Water Cherenkov Detector (1KT) Scintillating-fiber/Water sandwich Detector (SciFi) Lead Glass calorimeter (LG) before 2002 Scintillator Bar Detector (SciBar) after 2003 Muon Range Detector (MRD)

33. 33 SciBar neutrino interaction study Fully Active Fine-Grained detector (target: 16 tons of scint.). –Sensitive to a low momentum track. –Identify CCQE events and other interactions (non-QE) separately.

34. 34 NEUT: K2K Neutrino interaction MC CC quasi elastic (CCQE) –Smith and Moniz with M A =1.1GeV CC (resonance) single  (CC-1  ) –Rein and Sehgal’s with M A =1.1GeV DIS –GRV94 + JETSET with Bodek and Yang correction. CC coherent  –Rein&Sehgal with the cross section rescale by J. Marteau NC + Nuclear Effects  /E (10 -38 cm 2 /GeV) E (GeV)

35. 35 Oscillation signatures E. Aliu et al., Phys. Rev. Letters 94:081802, 2005.

36. 36 KAMLAND Reactor Experiment “Solar” neutrino oscillations in a controlled reactor-experiment

37. 37 Evidence for neutrino oscillations SK atmospheric K2K Solar experiments KAMLAND reactor exp.

38. 38 Neutrino oscillations: In addition to the Solar (+Kamland) and Atmospheric (+K2K), there are two other very relevant experiments:  Chooz reactor experiment. Sees no oscillation of reactor e over a baseline of 1 Km. conveniently ignored Excess of 87.9±22.4±6.0 events!  LSND accelerator experiment. Sees positive signal of oscillations of  → e over 30 m baseline

39. 39 Results of the analysis of the oscillation data

40. 40 Results of the analysis of the oscillation data

41. 41 Mixing angles:  12   sol  34º  2º  23   atm  45º  3º  13 < 12º (at 3  ) sin 2  13 ≡|U e3 | 2 < 0.04  m 2 atm ≡  m 2 32 =m 2 3 -m 2 2 =  [(2.4  0.3)x10 -3 eV 2 ]  m 2 sol ≡  m 2 21 =m 2 2 -m 2 1 = (0.8  0.3)x10 -5 eV 2 1  2/3 e 2  1/3 e 3  0% e Oscillation parameters

42. 42 In view of the results it is convenient to parameterize the PMNS matrix as: Parameterization of the PMNS matrix CP violation phase solar Links atmospheric & solar sectors atmospheric c ij ≡cos  ij s ij ≡sin  ij

43. 43 Solar Oscillations and the MSW effect The solar neutrinos pass through the very dense Sun core. Electron neutrinos can interact forward with the solar matter in two ways, while mu or tau neutrinos only do so through NC. Forward interactions cannot be distinguished from no-interaction at all  coherent scattering, which affects propagation through matter. The extra term for e gives an extra phase to mass eigenstates which interplays with that which gives rise to oscillations. The effect has the opposite sign for neutrinos and antineutrinos (has nothing to do with CP violation). eee e  e e e ZW

44. 44 Formulae are similar to those in vacuum with the replacement: + for neutrinos - for antineutrinos sign of  depends on sign of  m 2 Solar Oscillations and the MSW effect x > 1 x < cos2  12 P ee E  1 MeV

45. 45 Accelerator experiments and their primary goals: MiniBoone (FNAL): prove or disprove LSND K2K (KEK-Kamioka): check SK, improve  m MINOS (FNAL-Soudan) check SK, improve  m,  13 ? OPERA (CERN-LNGS) see  appearance in  beam T2K (KEK-Kamioka) try to measure  13... No a (FNAL-Nth Minn.) try to measure  13... Many ideas for future  13, CP-violation,... Near Term Longer Term

46. 46 Conclusions Neutrinos played a crucial role in establishing the Standard Model. Neutrinos have mass and mix. This is physics beyond the Standard Model. The masses and pattern of mixing is quite different from that of quarks. This may be a hint to the physics beyond the SM. Accelerator experiments permit the control of E, L and the initial neutrino state. They will have a role in elucidating fully the pattern of masses and mixings. Progress will require a variety of experiments at different energies and baselines.