1. Outline of lectures: 1)Status of the field: What we know for sure and what we should try to find out in near future? 2) Is the total lepton number conserved? Are neutrinos Dirac or Majorana fermions? 3) Exploring the consequences of finite neutrino mass: Neutrino magnetic moments, muon decay, beta decay. Scattered comments on particle physics models and the possible path to the SM. 4) Neutrinos in astrophysics and cosmology.

2. 1) Prehistory: `birth of neutrino’ : In nuclear  and  decay discrete lines were observed, however, the  spectrum of 210 Bi looked continuous (Chadwick 1914). The Q-value is 1161 keV, but the average  energy is only 337 keV (Meitner1930). This violated energy conservation. Also, the it was assumed that a nucleus, e.g. 14 N, was made of 14 protons and 7 electrons. Yet its statistics looked like BE, not FD. Way out was suggested by Pauli (famous letter, 12/4/1930), when he proposed the existence of neutrinos. Fermi (1934) formulated the theory of  decay. Neutrinos and electrons were created in the decay, not present beforehand. Bethe and Peierls (1934) estimated neutrino cross section as ~10 -44 cm 2, hence unobservable. Discovery of the neutron (Chadwick 32, Nobel Prize 1935)) solved the issue of statistics.

3. Estimate of the cross section: Take n -> p + e - + and consider + p -> n + e + At low (~MeV) energies the cross section can depend only on E (the energy of the neutrino or positron). Hence  ~ G F 2 E 2 (hc) 2. G F = 1.17 x 10 -11 MeV -2, hc = 2x10 -11 MeV cm Thus  ~ 10 -44 cm 2 (as in Bethe and Peierls) Reminder: Nuclei have R ~ a few x 10 -13 cm, nucleon Size is ~ 10 -13 cm  1 fm. Hence typical cross sections are  ~  r 2 ~ 10 -24 cm 2  barn. The low energy weak cross sections are ~20 orders of magnitude smaller.

4. 2) Early history: In 1953-56 Reines and Cowan detected electron antineutrinos from the nuclear reactor using reaction + p -> n + e + and observing the annihilation radiation in delayed coincidence with the neutron capture. The cross section agreed with expectations. Thus neutrinos became real particles. (Reines got the Nobel Prize in 1995). In 1956 Lee and Yang (Nobel Prize 1957) proposed that parity is not conserved in weak interactions. They were motivated by the study of K decays, which decayed both into two and three pion states, of opposite parity. The suggestion that parity is not conserved was quickly verified experimentally, by studies of  decay and  decay. The two-component neutrino theory (Lee & Yang, Salam, Landau 1957): The observed maximum parity violation in leptonic weak processes could be accommodated if neutrinos are massless (and hence helicity and chirality eigenstates). Only lefthanded neutrinos (and righthanded antineutrinos) would be needed. Lepton number would be conserved.

5. V-A theory: A priori it was not clear which of the possible Lorentz structures govern weak interactions, in particular S-T or V-A. The similarity of couplings in  and  decays lead to the formulation of the V-A model (Feynman & Gell-Mann, 1958). Of particular interest was the observation of the   -> e + + e decay. That decay is forbidden in the limit m e -> 0 for left-handed currents. Hence  e + )/  m e 2 /m  2 [m   - m e 2 ]/[m    m   ] = 1.284x10 -4 in perfect agreement with the experiment. Finally, the finding that the vector coupling constants (but not the axial ones) are the same (almost) in  and  decay lead to the conserved vector current hypothesis. All that set the stage for the Standard Electroweak Model of Glashow, Weinberg and Salam (Nobel Prize 1979).

6. Proof that is  different from e : Even earlier (Lokanathan & Steinberger 1955) the attempts to observe  e +  gave a small upper limit 2x10 -5 for the branch. That suggested that even though the weak coupling appeared to be universal, the  may be different from e. The way to prove it is to show that the reaction  + n ->  + p goes and  + n -> e  + p does not go. The proof was given by Danby et al. (1962, Nobel Prize 1988) who found that the beam of dominantly  from pion decay makes muons, but essentially no electrons (some were made from contaminants in the beam).

7. Discovery of neutral currents : The Standard Electroweak Model (Glashow 1961, Salam 1968, Weinberg 1967) predicted (among other things) the existence of neutral currents. They were observed through  + e  ->  + e   (observing recoiling electrons) at CERN (1973). The third lepton family  lepton) was discovered in 1975 at SLAC (Nobel Prize for Perl in 1995). An experimental proof of the existence of  was made only in 1999 (DONUT experiment). Standard Model postulates that all neutrinos are exactly massless. Individual lepton flavors are conserved, i.e. processes not only like  e +  but also  + n -> e -  + p etc. are strictly forbidden. However, more recent discoveries challenge this postulate and show that neutrinos are massive (albeit much lighter than other fermions) and that the individual lepton numbers are not conserved. Description of these phenomena will be the main topic of these lectures. It is hoped that the pattern of neutrino masses and mixing that is emerging will offer a glimpse into the fundamental source of particle masses and the role of flavor.

9. Oscillation phenomenology-quantum mechanical interference States with a definite flavor, e, , are superpositions of states 1, 2 with definite mass which propagate simply as plane waves. Atmospheric neutrinos, long baseline accelerator experiments Reactor searches for  13 Solar neutrinos, reactor verification of the solar neutrino oscillations. Propagation of a beam that began as e.

10. Dependence on the zenith angle, i.e. on the path length. Blue - no oscillations, red - with oscillations. Fit: sin 2 2  ~ 1,  m 2 ~ 2.5x10 -3 eV 2.  oscillate, presumably into , e is not affected. This finding later confirmed by accelerator experiments K2K and MINOS.

11. Since only few MeV neutrinos are involved, test of the `neutrino disappearance’ + ~180 km (Kamland)

12. Confirmation of the solar neutrino result, without matter effects and with antineutrinos

13. Kamland convincingly shows that e disappear and that the spectrum is distorted in a way only compatible with oscillations.

14. Effect of matter on neutrino propagation Oscillation of solar neutrinos: That is a preposterous idea; the mean free path is too long = 1/N , N = number density ~ N 0  ~ 10 24 cm -3,  = cross section ~ 10 -43 cm 2 for low energy neutrinos , thus, ~ 10 19 cm ~ 10 light years. The  is so small because it is ~ G F 2. But interaction energy with matter is ~ G F and might affect the relative phase of states that are not energy eigenstates. In matter the phase e -iEt, where E ~ p + m 2 /2p should be replaced by E +, where represents the expectation value of the weak interaction between the neutrinos and the constituents of matter. Thus in matter schematically E eff = E 0 + m 2 /2E 0 + 2 1/2 G F N e This term is present only for e and has a minus sign for e

15. All neutrinos interact equally through Z 0 exchange (NC) with electrons and quarks Electron neutrinos interact with electrons by Z 0 and W +- exchange

16. The matter oscillation length is therefore L 0 = 2  /2 1/2 G F N e = 1.7x10 7 (meters)/Y e  (g cm -3 ) Y e = Z/A (electron fraction) L 0 is independent of energy. For typical densities on Earth L 0 ~ Earth diameter so matter effects are small.However, in Sun or other astrophysical objects they are decisive. So, we can have two kinds of neutrino oscillations, vacuum and matter. To see which of them dominates, compare the two oscillation lengths: L osc /L 0 = 2 3/2 G F N e E /  m 2 = 0.22[E (MeV)][  Y e (100g cm -3 )][7x10 -5 /  m 2 (eV 2 )] If this ratio is >> 1 matter oscillations dominate, if it is <1, vacuum oscillations dominate.

17. For constant density case there can be three distinct regimes: 1)Low density, L 0 >> |L osc | : matter has little effect on oscillations 2)High density, L 0 H and oscillations are suppressed (since the amplitude ~ sin 2 2  m, where  m is the effective mixing angle in matter. 3)Resonance, when 22 1/2 EG F N e ->  m 2 cos2  v : in that case the oscillations are enhanced since  m ->  /4 independently of  v. Note that the resonance condition depends on the sign of  m 2, and whether neutrinos or antineutrinos are involved. The most interesting case is the case of neutrinos propagating through an object of varying density (e.g. the Sun) from the high density regime to the low density regime.

18. Edges of nonadiabacity Edges of matter effects

19. Expected fluxes of solar neutrinos (Bahcall) Components of the e flux (no oscillations) and ranges of the solar neutrino detection experiments are indicated. Note the extreme log. Scale.

20. Summary of results: Ratio of the observed/expected flux Ga, Cl, SNO CC,SK are charged current measurement, determine the flux of e only SNO NC is the neutral current. Determines the flux of all neutrinos Note: The Cl and SNO cc are below ~0.3. Ratio below 0.5 is impossible for two flavor vacuum oscillations. This is a clear indication of matter effects.

21. By combining the charged and neutral current events, SNO was able to show convincingly that the solar e were transformed into another active neutrino flavor. (Fluxes  in units of 10 6 cm -2 s -1 ) Shown are the SNO results from the 391 day salt phase.

22. Summary of the positive evidence:   oscillate into  with |  m 2 | ~ 2.4x10 -3 eV 2 and nearly maximum mixing angle (near 45 0 ). The sign of  m 2 remains unknown.  e oscillate into another active flavor with  m 2 ~ 8x10 -5 eV 2 and a large but not maximum mixing angle (  12 ~ 32 0 ). Because of the matter effects in the Sun, the sign of  m 2 is fixed (> 0 by convention, e are dominantly the lighter of the two). 3) But we do not know whether e are affected by oscillations with |  m 2 | ~ 2.4x10 -3 eV 2. If that effect exists, it is small.

23. What about the corresponding mixing angle    We have argued that the determination of the e component of atmospheric neutrino flux does not give very useful information on the angle  . The most natural way of determining that angle is to look for the e disappearance (or appearance) at distances corresponding to  m 2 atmos. Two such experiments with reactor antineutrinos, CHOOZ and Palo Verde were done in late nineties when it was unclear whether the atmospheric neutrinos involve     or   e. The characteristic distance is ~ km, and no effect was seen. Hence these result constrain    from above to rather small value.

24.  -3 eV 2 Constraints on   from the Chooz and Palo Verde reactor experiments. The region to the right of the curves is excluded. Note that the maximum sin 2  13 value depends on the so far poorly determined  m 31 2 value. Global fits give sin 2  13 = 0.9 -0.9 +2.3 x10 -2 at 95% CL, consistent with vanishing   

25. Present status of our knowledge of oscillation parameters or what do we know? 7.9 +0.4 -0.4 x 10 -5 eV 2 (2007) 2.38 -0.16 +0.2 x10 -3 eV 2 (2007)

26. The Mixing Matrix, decomposition into three simple rotations.

27. e [|U ei | 2 ]  [|U  i | 2 ]  [|U  i | 2 ] Normal Inverted  m 2 atm    (Mass) 2  m 2 sol }   m 2 atm    m 2 sol } or sin 2  13 The spectrum, showing its approximate flavor content (note that the absolute mass value remains undetermined)

28. Fly in the ointment: There were no (essentially) e in the neutrino beam, baseline = 30m Excess events: Oscillation probability: Decay at rest (DAR) signal backgrounds

29. For LSND L(m)/E(MeV) ~ 1 so the simple oscillation picture requires that  m 2 ~ 1 eV 2, clearly not compatible with the 3 neutrino picture with solar and atmospheric  m 2. Hence at least one sterile neutrino is required. To test this hypothesis the MiniBoone experiment at Fermilab used similar L/E but E = 500-1500 MeV (See Phys.Rev.Lett.98,231801)

30. MiniBoone data above the previously chosen threshold of 475 MeV are compatible with background. LSND oscillation signal not observed. 3006009001200 MeV

31. Pseudo discoveries (or claims that cannot be substantiated, at least so far) attract lots of attention: “30 eV neutrino of Lubimov” see V. Lubimov et al., Phys. Lett. B94, 266(1980) 285 citations “17 keV neutrino” see J.J.Simpson, Phys.Rev.Lett.54,1891(1985) 272 citations “Time variation of the solar neutrino flux” (this is not real measure since the “evidence” was not published separately, I use a theory paper instead) M.B.Voloshin et al, Sov.J.Nucl.Phys.44,44(1986) 145 citations “LSND oscillation evidence” see C. Athanassopoulos et al., Phys.Rev.Lett.77,3082(1996) 492 citations “Evidence for the 0  decay” (this has not been shown that it is incorrect, but it is controversial) see H.V.Klapdor-Kleingrothaus et alo., Mod.Phys.Lett.A16,2409(2001) 268 citations

32. Experimental goals for near future 1.Determine the mixing angle  13 2.Resolve the mass hierarchy (sign of  m 2 atm ) 3.Determine the Dirac CP phase  4.Determine how close is  23 to 45 0 5.Determine the absolute mass scale In order to solve the problems 1.-4. it is necessary to go beyond the 2 flavor picture and observe `subdominant’ oscillations, suppressed by one of the small parameters, sin 2 2  13 or  m 2 sol /  m 2 atm. The mass hierarchy can be resolved by matter effects. The CP violation is proportional to the product (Jarlskog invariant) sin 2 2  13 sin 2 2  12 sin 2 2  23 sin 2  m 2 21 L/E sin 2  m 2 31 L/E  sin 2  m 2 32 L/E sin 

33. MINOS experiment: Running since 3/2005. Results so far: |  m 2 23 | = 2.38 +0.20 -0.16 x 10 -3 eV 2, sin 2 2  23 > 0.87 (68%CL), and (v-c)/c = (5.1 2.9) x 10 -5.

34. at Gran Sasso

35. Determining  13 with reactor neutrinos: e survival probability with two oscillation lengths

36. Projected sensitivity of the Daya-Bay experiment (ultimately to sin 2 2  13 ~ 0.01)

37. Double Chooz experiment: projected sensitivity sin 2 2   

38. in a  beam

39. NO A experiment at Ash River, 810 km from FermiLab

40. Parameter degeneracy: There are several solutions with different  13, sign of hierarchy, CP phase  giving the same P(  -> e )

41. Reactor measurements of  13 will complement the long baseline exp.

42. DUSEL = Deep Underground Science and Engineering Laboratory The Homestake (South Dakota) site now chosen

44. The appearance of wrong sign muon represents golden measurement

45. The accelerated ions could be 6 He (T 1/2 = 0.8s, Q = 3.5MeV,    ~ 150  and 18 Ne (T 1/2 = 1.7s,Q = 4.4 MeV,  +,  ~ 60) with ~10 18 decays/year guaranteed pure e or e beams