Toyota 　 National 　 College 　 of 　 Technology

A.TakamuraCollaboration with

K.Kimura and H.Yokomakura

ICFP 2005

10/6 at National Central University

Enhancement of CP Violating terms for Neutrino Oscillation in Earth Matter

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

Atmospheric Neutrino

Solar Neutrino

CHOOZ

Present

Precious measurement of these small parameters is very important to discover CP

violation

Remark

Two small parameter

s

SuperbeamNeutrino Factory

Future

Long baseline

experiments

Matter Density Profile of the Earth

Preliminary Reference Earth Model

Analysis of matter effect in long baseline

experiments

Matter density is almost constant in L<5000 km

Remark

Matter density along neutrino path

Earth matter density can be approximated by three constant layers (mantle-core-mantle) in

L=12000km

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

Three layers

Mantle-core effect

Mantle MSW term

Core MSW term

Mantle-core term

RemarkMantle-core term is caused by the interference

between mantle and core

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

Two generations

Interference phenomenon between mantle and core

Numerical study of mantle-core effect

Remark Mantle-core effect can be larger than MSW effect

Solid, dashed, dash-dotted and dotted lines show probability, square of mantle, core, mantle-core terms,

respectively

Mantle MSW effect

Mantle-core effect

Core MSW effect

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

General feature of Hamiltonian

Standard parametrization

Three generations

CP dependence on probability is simple in arbitrary matter

Remark

Simple CP dependence

General relation

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

Enhancement of CP violating terms due to mantle and

core

Main result

Mantle-core effect of CP depending terms

Mantle-core effect

Mantle MSW

Core MSW

Remark Mantle-core effect seems to appear in CP violating terms, although effect is weakened

CP violating effects due to A and B　become large and can reach　 a few

10% of C

Mantle MSW

Core MSW

Mantle-core effect

Core MSW

Mantle-core effect

Mantle MSW

Application of three layer approximation

RemarkTwo generation

approximation makes calculation easy

similarly

Three layers

Application of High energy approximation

Approximate formula

High energy region

Remark Low energy function is simple in high energy region

Conclusion

Mantle-core term

ConclusionThe 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

Mantle-core effect

Mantle-core effect

Mantle-core effect