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

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

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

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

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

Mantle-core effect Mantle-core term is caused by the interference M. V. Chizhov and S. T. Petcov,Phys. Rev. D63 (2001) 073003 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

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

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

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

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

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

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

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

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

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

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