Post on 05-Jan-2016
description
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)