1. Neutrino Oscillation Nguyen Thanh Phong Yonsei Univ., May 19, 2008

2. Outline 1. Brief History of the Neutrino 2. The evidence of the oscillations of neutrinos 3. Theory of neutrino oscillation 4. Summary

3. 1. Brief History of the Neutrino 1) 1896: Henri Becquerel discovers natural radioactivity while studying phosphorescent properties of uranium salts. ‚  rays: easy to absorb, hard to bend, positive charged, mono-energetic; ‚  ray: harder to absorb, easy to bend, negative charge, spectrum?; ‚  rays: no charge, very hard to absorb. 2) 1897: J.J. Thompson discovers the electron.

4. 3)1911: Lise Meitner and Otto Hahn first shown that the energies of electrons mitted by beta decay had a continuous rather than discrete spectrum. 4) 1914: Chadwick presented definitive evidence for a continuous beta-ray spectrum. F. A. Scott, Phys. Rev. 48, 391 (1935) Instead of discrete  spectra were continuous

5. Origin continuous  -ray spectrum was unknown. Different options include several different energy loss mechanisms. It took 15 years more to decide that the “real” beta- ray spectrum was really continuous. Reason for continuous spectrum was a total mystery: + QM: Spectra are discrete; + Energy-momentum conservation: N → N’ + e - electron energy and momentum well defined

6. Nuclear physics before 1930: nucleus = n P P + n e e-  Example: 4 He = 4P +2e - work well.  However: 14 N = 14P +7e - is expected to be a fermion, but it was experimentally known that is a boson!  There was also a problem with the magnetic moment of nuclei:  N,  P   e (  =eh/4mc). How can the nuclear magnetic moment be so much smaller than the electron one if the nucleus contains electrons? SOLUTION: bound, nuclear electrons are very weird! + This can also be used to solve the continuous  -ray spectrum: energy need not to be conserved in nuclear processes! (N. Bohr) “…This would mean that the idea of energy and its conservation fails in dealing with processes involving the emission and capture of nuclear electrons. This does not sound improbable if we remember all that it has been said about peculiar properties of electrons in the nucleus.” (G. Gamow, 1931)

7. Enter the neutrino… Weakly interacting massless neutral fermion 1930: Postulated by Pauli: the "neutron", a new spin 1/2 particle with small mass and no electric charge in order that: + resolve the problem of continuous beta-ray spectra, + reconcile nuclear model with spin-statistics theorem. 1932: Chadwick discovered the neutron. Chadwick’s neutron if different from Pauli’s neutron = neutrino (Fermi).

8. Adapted summary of an English translation to Pauli’s letter dated December 4, 1930

9. observing the unobservable… 1) 1956: “Discovery” of the electron neutrino (Reines and Cowan) in the Savannah River Nuclear Reactor site. 2) 1962, the second neutrino:    e (Lederman, Steinberger, Schwarts at Brookhaven National Laboratory-BNL). First neutrino beam: 3) 2001:  directly observed (DONUT experiment at FERMILAB. Same strategy:

10. 2. The evidence of the oscillations of neutrinos A. Solar neutrinos B. Atmospheric neutrinos C. Nuclear reactor neutrinos

11. A. Solar neutrinos How the Sun burns

12. Solar neutrino deficit is now understood as a consequence of neutrinos oscillation.

13. A. Atmospheric neutrinos Atmosphere

14. (Sign of the particles are neglected in this figure.)

16. A half of  lost !!

17. B. Nuclear reactor neutrinos Reactor Long Baseline Experiment 150 - 210 km ( E pr > 2.6 MeV )

19. 3. Theory of neutrino oscillation A. Neutrino oscillation in vacuum B. Neutrino oscillation in matter

20. Neutrinos come from at least three flavors The known three flavors: Each of these is associated with the corresponding charged-lepton flavor: The meaning of this association

21. Over short distance, neutrinos do not change flavor: Does not occur But if neutrinos have masses, and leptons mix, neutrino flavor changes do occur during long journeys

22. Let us assume neutrino have mass and leptons mix When W + decays: The produced neutrino state |  > is Neutrino of flavor  Neutrino of definite mass m i Lepton mixing matrix

23. Another way to look at W boson decay A given l  + can be accompanied by any i, and The neutrino state |  > produced together with l  + is

24. According to the Standard Model, extended to include neutrino mass and leptonic mixing  The number of different i is the same as the number of different l  (3).  The mixing matrix U is 3 x 3 and unitary: UU †  = U † U = 1 From |  > = Σ i U*  i | i > and the unitarity of U, The flavor-α fraction of i is

25. Neutrino Flavor Change (Oscillation) in Vacuum

26. What is Propagator ( i )  Prop( i )? | i,L  = exp[ -i(E i t - p i L)] | I,o  Neutrino sources are ~ constant in time. Averaged over time of the interference is Unless E 1 = E 2 Only neutrino mass eigenstates with a common energy E are coherent.

27. For each mass eigenstate | i,L  = exp[-im i 2 L/2E)] | I,o 

28. Probability for Neutrino Oscillation in Vacuum

29. For Antineutrinos: We assume the world is CPT invariant.

30. — Comments — 1. If all m i = 0, so that all Δm ij 2 = 0, Flavor changes  mass 2. If there is no mixing, Flavor changes ⇒ Mixing

31. 3. P (  →  ) depends only on squared-mass splittings. Oscillation experiments cannot tell us 4. Neutrino flavor change does not change the total flux in a beam. It just redistributes it among flavors

32. When There are Only Two Flavors and Two Mass Eigenstates

33. The oscillations of neutrinos in matter Hamiltonian of a neutrino in a medium: H = H 0 + V, V = V NC + V CC  const.*I + V e CC (Up to small higher-order corrections)

34. 2 oscillation in constant-density matter

35. — Comments — 1) Mikheyev - Smirnov - Wolfenstein (MSW) resonance: 2) For anti-neutrinos, V e CC changes sign, hence there is no MSW resonance for anti-neutrinos 3) Matter effects induces the CP violation for 2 oscillation in a medium.

36. Summary The history of neutrino is briefly introduced. Some evidences of the oscillations of solar neutrino, atmospheric neutrino and nuclear reactor neutrino are shown. The theory of neutrino oscillation in vacuum is derived. The interaction of neutrinos with medium is introduced, and 2- family neutrinos oscillation in constant density matter is considered. We see that the CP-violation can induced from the effect of matter which is absented in vacuum.