1. Matter Effects on Neutrino Oscillations By G.-L. Lin NCTU Nov. 20, 04 AS

2. Outline Matter effects and Solar Neutrinos The world with  13 and matter enhancement to  13 Very Long Baseline Neutrino Oscillation Experiments and the Determination of  13 and  23 —work in progress with Y. Umeda

3. The Neutrino Mixing Matrix The world without  13 and  CHOOZ bound sin 2 2  13 < 0.1

4. Neutrino-electron coherent scattering

5. Solar Neutrino Oscillations and Matter Enhancement Diagonalization:  12   12 m

6. Wolfenstein, 1978 Mikheyev and Smirnov, 1986 Varying electron density in the Sun Adiabaticity

7. Combine Solar Neutrino and KamLAND experiments: Y.-F. Wang in ICHEP04

8. The World with  13 new mixing! The e   oscillation length: For an experiment with the terrestrial beam E  a few GeV, one drops

9.  does not evolve, while e  + induced by  13 and A e. Diagonalization:  13   13 m

10. Earth mantle:  =5 g/cm 3, E res  6.4 GeV Earth core:  =12 g/cm 3, E res  2.7 GeV Barger et al., 99 Banuls, Barenboim, Bernabeu, 01

11. Stacey, Physics of the Earth, 77 Freund and Ohlsson 99  m =5 g/cm 3  c =12 g/cm 3

12. Very Long Baseline Neutrino Oscillation Experiments The solution the equation in the constant-density approximation: In progress with Y. Umeda Still treat  =0

13. Use actual Earth density profile for calculation

14. How long is the “very long” baseline? Banuls, Barenboim, Bernabeu, 01  Optimized for P(   e )  1-P(    ) also peaks at E  E res Gandhi et al., hep-ph/0408361

15.  Simultaneous measurements of P(   e ) and P(    ): sensitive to  13 and  23. Are they really Independent?  P(   e ) studied for L=9300 km— Fermilab to Kamioka. F. DeJongh, hep-ex/0203005 Consider L=9300 km case for P(   e )  P  e and P(    )  P 

17. In progress with Y. Umeda

23. < 0.03 >0.03 w.r.t resonant energy

24. Issues to be considered:  The effect of CPV phase  (  10%, Gandhi et al., hep-ph/0408361 )  Convoluting with the  spectrum from the accelerator

25. . DeJongh, hep-ex/0203005  CC events before and after oscillations Sharp cutoff to avoid background

28. From the mixing matrix, one derives

29. Studying GeV neutrinos on Earth