1. Enhancement of CP Violating terms
ICFP 2005
Enhancement of CP Violating terms
for Neutrino Oscillation in Earth Matter
10/6 at National Central University
Toyota　National　College　of　Technology
A.Takamura
Collaboration with
K.Kimura and H.Yokomakura

2. Outline of this talk Introduction to neutrino oscillation
Mantle-core effect in Earth matter
General feature of CP dependence
Enhancement of CP violating terms due to mantle and core
Main result

3. Introduction to Neutrino Oscillation
Present
Superbeam
Neutrino Factory
Future
Long baseline experiments
Atmospheric Neutrino
Solar Neutrino
CHOOZ
Two small parameters
Precious measurement of these small parameters is very important to discover CP violation
Remark

4. Matter Density Profile of the Earth
Matter density is almost constant in L<5000 km
Remark
Matter density along neutrino path
Preliminary Reference Earth Model
Earth matter density can be approximated by three constant layers (mantle-core-mantle) in L=12000km
Analysis of matter effect in long baseline experiments

5. Outline of this talk Introduction to neutrino oscillation
Mantle-core effect in Earth matter
General feature of CP dependence
Main result
Enhancement of CP violating terms due to mantle and core

6. Mantle-core effect Mantle-core term is caused by the interference
M. V. Chizhov and S. T. Petcov,Phys. Rev. D63 (2001)
E. Kh. Akhmedov, A. Dighe, P. Lipari and A. Yu. SmirnovNucl. Phys. B542 (1999) 3
Interference phenomenon between mantle and core
Two generations
Three layers
Mantle MSW term
Core MSW term
Mantle-core term
Remark
Mantle-core term is caused by the interference
between mantle and core

7. Numerical study of mantle-core effect
Mantle MSW effect
Core MSW effect
Mantle-core effect
Solid, dashed, dash-dotted and dotted lines show probability, square of mantle, core, mantle-core terms, respectively
Remark
Mantle-core effect can be larger than MSW effect

8. Outline of this talk Introduction to neutrino oscillation
Mantle-core effect in Earth matter
General feature of CP dependence
Main result
Enhancement of CP violating terms due to mantle and core

9. General feature of Hamiltonian
Three generations
General relation
Standard parametrization
Simple CP dependence
CP dependence on probability is simple in arbitrary matter
Remark

10. Approximation of two amplitudes
Two amplitudes can be approximated by those in the vanishing limit of small parameter
Remark

11. Low and High Energy Hamiltonians
Vanishing limit of
Vanishing limit of
Remark
Two amplitudes can be approximated by those in two generations

12. Outline of this talk Introduction to neutrino oscillation
Mantle-core effect in Earth matter
General feature of CP dependence
Main result
Enhancement of CP violating terms due to mantle and core

13. Mantle-core effect of CP depending terms
Mantle MSW
Core MSW
Mantle-core effect
Mantle-core effect
Mantle MSW
Core MSW
CP violating effects due to A and B　become large and can reach　a few 10% of C
Remark
Mantle-core effect seems to appear in CP violating terms, although effect is weakened

14. Application of three layer approximation
Three layers
Remark
Two generation approximation makes calculation easy
similarly

15. Application of High energy approximation
Approximate formula
High energy region
Remark
Low energy function is simple in high energy region

16. Conclusion Conclusion Mantle-core term
Mantle-core effect
Mantle-core effect
Mantle-core effect
Mantle-core term
Conclusion
The mantle-core effect, which is different from the usual MSW effect, appears not only in C but also in A and B, although the effect is weakened