The earth matter effect in T2KK

Based on work with K. Hagiwara, N. Okamura @KEK

Ken-ichi SendaGrad. Univ. for Adv. Studies

&KEK

Matter effect and mass hierarchy-Why the matter effect is important?-

eeRCTATMe BAP

2sin)1(sinsin4 13222

LE

mijij 2

2

MNSRCT

SOLATM

MNSRCT

SOLATMe

E

aL

m

aA

cossin4

sintan

4B

sinsin2

sintan

2

2

12e

2

12213

matter effect CP phaseThe sign of the matter effect term in Ae depends on that of δm2

13

→ One detector experiment cannot solve the correlation between sinθRCT and the matter effect. In T2KK, this correlation is solved by comparing two oscillation amplitudes with same L/E but different energy (distance).

GeV/eV 1056.7

325 E

cmga

Seismic wave reflection

• One of the method to survey the undergrounds is measurement of the seismic (sound) wave reflection.

• The origin of the error to the density is mainly uncertainty of the model which converts the sound velocity to the average density.In LND model, the uncertainty of the conversion is about 6%.

This error is expected to be smaller by combining the other type measurements.

Ludwig, Nafe, Drake (1970)

ec) wave(km/sseismic theofvelocity :

7.023.2598.00704.000283.0]/[ 2343

V

VVVVcmg

Seismic wave data around the baseline

Zhao, Horiuchi, Hasegawa

Tectonophys. (1992)

Sato et. al.

Geohys. Geochemi. Geosys (2006)

H-J. Kim et. al.

Tectonophys. (2003)

H-M. Cho et. al.

Geophys. Res. Lett (2006)

Matter profile along the baselines

Tokai-to-Kamioka case

Tokai-to-Korea case

Main layer where the neutrino travels

mud stone layer ： 2.5 g/cm 3

upper crust ： 2.8g/cm 3

average density ： 2.6g/cm 3

error ±6%

Main layer where the neutrino travels

upper crust ： 2.8g/cm 3

lower crust ： 2.9g/cm 3

upper mantle ： 3.3g/cm 3

average density ： 2.98g/cm3 (L = 1000km)

3.03g/cm3 (L = 1200km)

error: ±6% ( ～ 0.18g/cm3)

The effect of the matter distributionThe difference between the highest density and the lowest density in the cross

section view ： 　　　　　　 about 11% to the average for Tokai-to-Kamioka, about 17% for

Tokai-to-Korea →Is there any effects of the matter distribution ?Such effects in the K2K experiment was studied by the Fourier expansion. [M. Koike, J. Sato, Mod. Phys. Lett. A (1997)]

,

4

8)Im(

4

4)Re(

2sin)1(sinsin4

2213

20

1

2

22213

22

213

22213

213

213

13222

m

aOB

k

k

m

a

km

aA

BBAAP

k

kk

eerctatme

10

2 2sinIm

2cosRe2)(

kkk

n

xL

ni

n xL

kx

L

kex

averagesymmetric distribution asymmetric distribution

●The only real part of ak in Ae gives non-negligible contribution.●That term is sensitive to the mass hierarchy.●Because of factor 1/k2, large k modes is not important.

GeV/eV 1056.7

325 E

cmga kk

Fourier modes of the density distribution

Tokai-to-Kamioka case

Tokai-to-Korea case

Largest coefficient ： [Reρ1]/ρ0 = 1%

distribution: symmetric

　　　　　　　　→ The real parts are large. 　　　　　　　　

Largest coefficient ：　（ L=1000km ） [Reρ1]/ρ0 =-3.3 %

The effect on χ2 analysisPrevious work (hep-ph/0607255)detector in Korea: 100kt Water cerenkov

running time: 5years (5.0×1021 POT)

density: 2.8 g/cm3 (Tokai-to-Kamioka)

3.0 g/cm3(Tokai-to-Korea)

error of density: 3%

Fourier mode: not included

The best combination to determine the neutrino mass hierarchy

→3.0°@SK, 0.5°@Korea （ L=1000km ）Δχ2 = 22.2

We check the effect of changing the conditions for the matter density to the Δχ2 of this combination.OLD ρSK 2.8

→2.6g/cm3

+

error 3%→6% + Fourier mode

Total

Δχ2=22.2

+0.6 -0.6 +0.5 22.7The difference of the matter effect gets large.

Larger error makes the Δχ2 smaller

Fourier mode helps determining the sign of Δ13

Summary

● We estimate the matter distribution along the baseline from the recent seismic wave analysis.

● The main origin of the error is uncertainty of the velocity-density conversion, 6%.

● Average density: Tokai-to-Kamioka 2.6 g/cm3 ± 6%

Tokai-to-Korea 3.0 g/cm3 ± 6%● We find the Fourier mode along the baseline is

important as well as the error to the average matter density:

　　 [Re(ρ1)/ρ0]: Tokai-to-Kamioka: 1%

Tokai-to-Korea: 3.3%● The effect of the earth matter effect in chi square

analysis.OLD ρSK 2.8 →2.6g/cm3

+

error 3%→6% + Fourier mode

Total

Δχ2=22.2

+0.6 -0.6 +0.5 22.7

Tokai-to-Kamioka-and-Korea experiment

OAB 3.0 @ SK

Down side of the T2K beam will appear in Korea while the T2K is running.

→ We can operate two LBL experiments, Tokai-to-Kamioka and Tokai-to-Korea.

mass hierarchy and the matter effect in T2KK

When we choose the combinatino of the off-axis angles as SK:2.5°-3°, Korea ：0.5°-1.0°, we can compare the amplitudes near the oscillation maximum.

)(sinsin4

)|(|)|(|)|(|P

213

22

131313

SKKrrctatm

SKe

Kre

aam

PP

The difference of the amplitudes near the oscillation maximum.

2

2

213

22

2

13132

)()(

sinsin4

)(

)0()0(

SKKrrctatm aaPm

P

PP

Significance to the mass hierarchy pattern (rough estimation)