1. Present and future experiments on neutrino masses and mixing Petr Vogel, Caltech 1.Recent triumphs. Where are we? 2.Planned refinements. Looking for symmetries and possible CP symmetry violation. 3.Are neutrinos Majorana particles? How can we tell? And how light neutrinos really are? Heraeus Summer School, Dresden, Aug. 29 - Sept 7, 2005

2. Note: Throughout references are used sparingly (my apologies to those not quoted properly) Summaries of the field, with references, can be found at e.g. 1)APS Multidivisional Neutrino Study /www.aps.org/neutrino/ 2) Neutrino Telescopes, Venice 2005 /axpd24.pd.infn.it/conference2005/talks/Venezia_talks.htm 3) Neutrino 2004, Paris, June 14-19 /neutrino2004.in2p3.fr/ There are many review papers, again with apologies let me quote our own, R.D.McKeown and P.Vogel, Phys.Rep.394,315(2004)

3. First lesson: Quantum mechanics works! (or in other words, phases matter) In the standard electroweak model neutrinos are massless and the lepton flavors are exactly conserved. Formally this is a consequence of the absence of the right-handed weak singlet components. Neutrino masses do not arise even through loop effects. Charged lepton and neutrino fields form doublets in SU(2) L: Lets assume that this is not so, and that neutrinos are massive, and that the above flavor eigenstates are coherent superpositions of states with definite masses, socalled mass eigenstates.

4. Thus And the states i propagate as plane waves, for E>>m i (common phase is skipped) The flavor is no longer conserved, and the transition amplitude is Transition probability is an oscillating function of the distance

5. When only two flavors (and mass eigenstates) exist, there is only one mass square difference  m 2 and only one mixing parameter   The oscillation probability is then and the characteristic oscillation length is,. For three neutrino flavors there are 3 mixing angles       one Dirac phase  and two Majorana phases      The mixing matrix (often called PMNS or MNS) is then written as Obviously, there are no oscillations when  m 2 =0, or  or 

6. By observing oscillations one can then determine (at least in principle) the corresponding fundamental parameters: a)Two mass squared differences  m 21 2,  m 31 2 b)Three mixing angles       c) CP violating phase  d)Majorana CP violating phases      which affect only processes that violate total L) We will see shortly what has been done so far in that respect, and what remains to be done.

7. But first we should, however, discuss what happens when neutrinos propagate in matter. In matter neutrinos of all flavors interact equally with the electrons and quarks by the Z exchange, but only e interact with electrons by the W exchange. Thus, an additional phase appears and a corresponding matter oscillation length To see what happens, one has to solve the corresponding equations of motion which for 2 flavors is of the form

8. Schematic illustration of the survival probability of e created at the solar center. The labels are sin 2 2  values. Note the possible suppression of P in particular for small  This is the famous MSW effect.

9. Second lesson: Neutrino oscillations are real. We are lucky enough that the oscillation parameters are such, that this is possible. Even though we know that there are (at least) three flavors all observations up to now can be analysed in the two flavor context (we will see shortly why this is so). Interestingly, oscillation phenomena were found `by accident’, in experiments designed to observe something else, and with `natural’ sources of neutrinos. (Remember Becquerel’s discovery of radioactivity or Anderson’s discovery of the muon.)

10. Atmospheric neutrinos: Angle   and the mass difference  m 31 2 ~  m 32 2. Cosmic ray protons and nuclei interact with the nitrogen and oxygen in the upper atmosphere, and produce (dominantly) pions. These, in turn, decay,  Most of the muons also decay, and one thus expects the ratio of   e events to be ~2. Also, by determining the zenith angle of the incoming neutrinos, one can study the path length dependence of the results. Atmospheric neutrinos were observed in a number of detectors, most of which were built to study proton decay. Most of them can distinguish between  and e like events (but not between and 

11. Illustration of the relation between the zenith angle and flight path (from V. Barger et al.)

12. upgoing downgoing S-K I: 1489 live-days, 100 yr MC,15,000 neutrino events Recent Atmospheric Sector Measurements  Zenith angle distributions showing  disappearance M. Vagins, EPS/HEPP2005 Red MC no osc. Green MC with oscillations

13. upgoing downgoing S-K II: 627 live-days M. Vagins, EPS/HEPP2005 Recent Atmospheric Sector Measurements  Zenith angle distributions showing  disappearance

14. What does it mean? Clearly, the  flux is less than expectations, in particular for the upward going neutrinos, while the e flux is in agreement. This finding is also supported (was preceded) by the determination of the `double ratio’ (   e ) exp / (   e ) MC ~ 0.6. Fits suggest that  and  are essentially maximally mixed, i.e. sin 2      and that |  m 31 2| ~|  m 32 2 | = 2.4 -0.6 +0.5 x10 -3 eV 2 (note that for such  m 2 and E ~ 1 GeV, L osc ~ 1000 km, corresponding approximately to cos  anthropic principle’?).  `disappearance’ has been confirmed by the K2K accelerator experiment (260 km distance) where 107 events were observed (151 expected) (Aliu et al, Phys.Rev.Lett. 94,081802(2005)) Atmospheric neutrino results, with nearly maximal   and with   e ~2 are insensitive to the mixing between e and other flavor (i.e. to   . This is so, because in such situation the     and e fluxes are almost equal, and therefore unaffected by oscillations.

18. Solar and reactor neutrinos: Angle   and mass difference  m 21 2 Predicted (SSM) solar e spectrum. thresholds of the Various experiments are indicated.

19. Results of different experiments (as ratios to SSM) ordered according to their their thresholds. Filled circles - exp. Data. Open circles - best fit to oscillations.

20. Schematic illustration of the survival probability of e created at the solar center. The labels are sin 2 2  values. pp 7 Be 8B8B

21. Measured charged current (CC), neutral current (NC) and elastic scattering (ES) from SNO, together with the SSM prediction.

22. The only way one can interpret the solar neutrino results is by invoking the idea of neutrino oscillations enhanced by the matter effects. Even though only the 8 B neutrinos (~10 -4 fraction of the total solar e flux) has been observed in `live’ experiments, it is impossible to explain the findings by some hypothetical flaws in the solar model. Moreover, the suppression factor ~1/3, can be understood only if the matter effects play a decisive role. Interpreting the results as oscillations, we arrive at the following parameters:  m 21 2 ~ 10 -4 eV 2,  sin 2    ~ 0.31 (large but not maximal). Note that the matter effects depend on the sign of  m 2, hence we know that m 2 > m 1. The decisive confirmation of the oscillation hypothesis involving e and  e comes from the reactor experiment KamLAND.

23. In fact, solar neutrinos (from 8 B decay observed in SK and SNO) actually “do not oscillate”. They are born as the heavier eigenstate  and propagate like that all the way to a detector. The fact that the oscillation parameters derived from the solar e  and reactor e agree is a sign of not only CPT invariance but test the whole concept of vacuum and matter oscillations. Two comments: Since solar density, and e energies, are fixed, it is fortuitous that the parameter  m 21 2 ~ 10 -4 eV 2 > 0 is such that we can observe the rich phenomena of matter oscillations. (Another example of `anthropic principle’ ?)

24. Nuclear reactors produce  e isotropically in the  -decay of neutron-rich fission fragments. A typical 3 GW power reactor produces ~6x10 20  e /s. A convenient way of detecting reactor  e is by using the relatively large and well understood cross section of the inverse neutron  decay,  e + p -> n + e +, and its correlated signal. An example for 12 tons detector 0.8 km from a 12 GW th power reactor.

25. So far all reactor experiments relied on the known e spectrum, and measured the signal at a given distance L. Since the energies are fixed, the distance L defines the sensitivity region for  m 2.

27. From Araki et al. (KamLAND coll.) Phys. Rev. Lett. 94, 081801 (2005) One can see that not only is the total rate less than expected, but there is evidence for spectrum distortion that allows one to determine  m 21 2 = 7.9 -0.5 +0.6 x10 -5 eV 2 in agreement, but more accurate, than the solar result.

28.  `interferometry’ probes flavor non-diagonal processes For example, when traveling through matter: (for ’s, we can treat bulk matter as just a potential term!) Simple approach:

29. ReactorSolar E 2-10 MeV 0.1-15 MeV L150 km1.5 x 10 8 km MSW No Yes Anti- e e Only(?) Standard Model couplings predict that these 2 experimental regimes will see the same effect  KamLAND+SNO: Testing the Model KamLAND, PRL 94, 2005

30. What about the 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.

31.  -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   

32. Preliminary conclusions: 1)The existence of neutrino mass and mixing has been convincingly established. Lepton flavor is not conserved. A window to physics beyond the SM has been opened. 2)Assuming that only 3 flavor and mass eigenstates play a role (careful, we will comment on this shortly), the elements of the mixing matrix and the mass squared differences have been determined (albeit some with rather large error bars). 3)The mixing matrix is, surprisingly, unlike the CKM matrix for quarks, which is `nearly’ diagonal. In contrast, the neutrino mixing matrix has two large mixing angles. The neutrino masses are very small compared to the charged fermions, and their pattern is also different. 4)Note, however, that there appear to be two small parameters,  m 2 sol /  m 2 atm ~ 1/30 and sin 2 2  13 0.09.

33. The neutrino sector is really strange….

34. (entries evaluated for U e3 = 0.1, near the middle of allowed range) The neutrino sector is really strange….

35. Three-flavor fit of oscillation parameters (Fogli et al. hep-ph/0506083, errors 95%CL)  m 21 2 = 7.92 -0.71 +0.71 x 10 -5 eV 2  m 31 2 = 2.4 -0.62 +0.50 x 10 -3 eV 2 sin 2  12 =0.314 -0.047 +0.057 (substantially less than 0.5) sin 2   = 0.44 -0.10 +0.18 (compatible with 0.5) sin 2   = 0.9 -0.9 +2.3 x 10 -2 (compatible with 0.0)

36. LSND – fly in the ointment L = 30 m, E  = 20-50 MeV, “decay at rest spectrum” Oscillations    ->  e, 87.9 +- 22.4 +- 6.0 events, oscillation probability 0.264 +- 0.067 +- 0.45 % Most of the parameter range excluded by reactor and KARMEN experiments, but a sliver with 0.2 <  m 2 < 10 eV 2 remains. Requires existence of sterile neutrinos !!! At present tested by Mini-BOONE at Fermilab, wait and see……(until late 2005 at least, probably even later) Third lesson: Not everything is simple, or

37. Decay at rest spectra:       monoenergetic    e + + e +   `Michel spectra’   are produced less and do not decay weakly, instead they form a pionic atom and are absorbed by strong interaction. Thus  e are missing

40. But we know that there are only 3 `active’ neutrinos. If indeed (at least) one light `sterile’ neutrino exists, all bets are off. Thus, we shall wait (eagerly) for the MiniBoone result, and reserve judgment for now. Numerous attempts to fit all existing data (including LSND) in schemes 3+1 or 2+2 etc. are `disfavored’, i.e. the fit is not too good.

41. e [|U ei | 2 ]  [|U  i | 2 ]  [|U  i | 2 ] NormalInverted  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, is So, here is once more what we know (dismissing LSND for now): Slide by B. Kayser

42. So what are the remaining issues? a)Qualitative: What is the sign of  m 2 atm ? Is the angle   nonvanishing, or can one hope to observe CP violation of leptons? Are neutrinos Majorana particles, or, is the total lepton number conserved? What is the absolute mass scale? Are there other surprises? b) Quantitative: Measure the magnitude of    Is   exactly 45 0 ? (    symmetry) Measure  m 2 atm more accurately. We will discuss black issues in the second lecture, and purple issues in the third lecture.