1. Neutrino Masses and Mixings
Kenzo Ishikawa　
OMEGA０７
Department of Physics
Hokkaido University

2. Topics 1. Neutrino Parameters 2. Finite coherent length effects
in “scattering of extremely high-energy charged particle with cosmic backgrond radiation “ (collaboration with Y. Tobita)

3. 1. Neutrino parameters Quarks and leptons of standard model
Three familys of quarks and leptons

4. Particle table in the standard model
Quarks
Leptons

5. Three family of matter 1st generation e neutrino u-quark e d-quark
2nd generation
μ-neutrino c-quark
μ s-quark
3rd generation
τ-neutrino t-quark
τ b-quark

6. Masses of Quarks and Leptons
Quarks and charged lepoton
mass
neutrino
generations

7. Atmospheric
Solar

8. excluded?

9. Oscillation formula from mass eigenstate to flavor eigenstate
From rest frame to laboratory frame
Local coordinates
Relativistic energy

10. Phase of mass eigenstate
Flavour wave function
Transition probability
Physical units

11. distance vs energy (vacuum oscillation)
|m1^2-m2^2|=1 ev^2
E(GeV)
L(Km)
|m1^2-m2^2|=10^(-3) ev^2
E(GeV) ^(-3)
L(Km) ^2 10^3 10^4
|m1^2-m2^2|=10^(-5) ev^2
E(GeV) 10^(-3)
L(Km) ^ ^3 10^ ^6
R(earth)=6x10^4 Km , L(sun-earth)=1.4x10^8 Km

12. Quasi-two-neutrino oscillation
here
And

13. Matter MSW effect
Electron neutrino has additional contribution from the charged elastic scattering and the finite electron density

14. Local positions
Neutrino oscillation amplitude is written by one particle wave function,
because
1. neutrino interacts with matter weakly
2. production and detection positions are localy defined

15. Experiments 1 Sun; Davis ,SK(Super Kamioka),SNO
2 Atmosphere; K(Kamioka),SK
3 Accelarator ; K2K(KEK-Kamioka),
4 Reactor ; Kamland,

16. 1.Solar neutrino

17. Solar neutrino summary
groups targets unit expement expectation ex./SSM
Homestake Cl SNU ± ±0.03
SAGE Ga SNU ± ±0.04
GALLEX Ga SNU ± ±0.04
SKe (water) /cm2/s 2.35± ±0.02
SNO pure D2O 106/cm2/s ± ±0.02
SNO salt (D2O) 106/cm2/s ± ±0.08
SNU = Solar Neutrino Unit = Events / 1036 atom / sec

18. SNO Detection of neutral current by
Flux ratio of elastic event vs total neutrino evevts

19. 2. Atmospheric neutrino
Observe electron neutrino event and muon neutrino event .
Find the deficit of muon neutrino flux

20. 3. K2K(long base line exp.) Event Summary
K2K-I+II
Nskobs
Nskpred
FC in 22.5kt
112
155.9
　1ring 67
99.0
　　m-like 58
90.8
　　e-like 9
8.2
　Multi Ring 45
56.8
Nskobs systematics ~3%
Fiducial volume 2%
Reduction <1%
Others <1%
Nskobs Spectrum syst. (1 ring m)
(dependent on the energy bin)
Ring counting ~3~5%
Fiducial volume 2%
Particle Id <1%
Energy scale ~2%
Nskpred systematics
Far/Near ～5%
Normalization ～5%

21. 4. Kamland(reactor neutrino)

22. Summary of masses and mixing 1

23. Summary of masses and mixing 2
Atmospheric
Solar+reactor(long distance)
Reactor (short distance)

24. Mass hierarchy
tau
electron
muon

25. Or inverted mass hierarchy ?

26. Other (recent) experiments
T2K J-park (Tokai) > Sk(kamioka)
Minos(USA), Borexino(Italy), Opera(Cern-Italy),Nova(USA),- - -
Neutrino telescope
Icecube(J), Goldstone(Moon),
Other proposals.

27. T2K (Tokai to Kamioka)
2008

28. Tokai 2 Korea may resolve hierarchy problem
K.Hagiwara et al,hep-ph/

29. Open problems Absolute values of masses
Other components of mixing matrix U
Is neutrino Majorana or Dirac ?
neutrinoless double Beta decay
Can we use neutrino for astronimical observations ?
Implications and theorｙ

31. Neutrino in the intermediate state
beam
target
Asahara,KI,Shimomura,Yabuki,PTP１１３，２００５

33. 2. Finite coherent length effect
in “scattering of extremely high-energy charged particle with cosmic backgrond radiation “
(collaboration with Y. Tobita)
Ref. on wave packet
K.I and T.Shimomura ,PTP１１４（２００５）

34. Wave packet with finite coherent length
Wave packet size is semi-microscopic and its effect is normally negligible, because
delta p( or E)(wave packet)<< delta p(orE )(exp.)
However if wave packet effects are enhanced by aother mechanism, a finite wave packet effects is possible.

35. Extremely high energy particle
(p+q)^2=m1^2+m2^2+2p q
=m1^2+m2^2+2 p0q0(1-a )
Delta q0(wave packet) << delta q(exp)
However If p0 >> m, (extremely high energy)
p0q0 >> (delta E(exp.))^2

36. Cosmic ray’s flux
Ultara-high energy

37. GZK bound High energy proton +2.7K Gamma > nuclean +pion
GZK estimated pion production cross section due to Delta resonance(1236).
Mean free path becomes about 10 Mpc, and cosmic rays beyond this threshold 10^20eV should be suppressed .(GZK bound)

38. AGASA
Fly’sEye,PierreAugerColla.Tele.Arrays

39. Finite coherent length of cosmic gamma
Wave packet
Plank distribution
Mean crossection

40. Comparisons of mean free path
Wave packets
Plane waves

41. Summary New era on neutrino masses and mixing.
Masses and mixing parameteres are fundamental physical constants and it is important to know their precise values.
Neutrino masses and mixing would play key roles for the physics beyond the standard model.
Wave packet effects may be important
in UHCR .