Download 2.8 g/cm 3

The earth matter effect in T2KK
Ken-ichi Senda
Grad. Univ. for Adv. Studies
&KEK
Based on work with K. Hagiwara, N. Okamura @KEK
Matter effect and mass hierarchy
-Why the matter effect is important?-
 13
e
P e  4 sin  ATM sin  RCT (1  A ) sin 
B 
 2

2
2
e
2
mij2
 ij 
L
2E
   E 

a  7.56 10 5 eV 2 

3 
g
/
cm
GeV



tan  ATM sin  SOL
2a
A  2  12
sin  MNS
m13
2 sin  RCT
2
e
tan  ATM sin  SOL
aL
B 
 12
cos  MNS
4E
4 sin  RCT
2
e
matter effect
CP phase
The sign of the matter effect term in Ae depends on that of δm213
→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).
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)
[ g / cm3 ]  0.00283V 4  0.0704V 3  0.598V 2  2.23V  0.7
V : velocity of the seismic wave(km/s ec)
Seismic wave data around the baseline
H-J. Kim et. al.
Tectonophys. (2003)
Sato et. al.
Geohys. Geochemi.
Geosys (2006)
H-M. Cho et.
al.
Geophys. Res.
Lett (2006)
Zhao, Horiuchi, Hasegawa
Tectonophys. (1992)
Matter profile along the baselines
Tokai-to-Kamioka 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%
Tokai-to-Korea case
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 distribution
The 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)]
 ( x) 

 ne
i
2 n
x
L
n  

 2k
  0  2 Re  k cos
 L
k 1 
average


 2k
x   Im  k sin 

 L
symmetric distribution
asymmetric distribution
  k  E 

ak  7.56 105 eV 2 

3 
 g / cm  GeV 


P e  4 sin 2  atm sin 2  rct (1  Ae  A) sin 2  13  Be  B 
 2

2
2
2 2

 Im( ak )
 
413
8k 
 Re( ak )

A   


2
2
2
2
2 2
2 2 

m

m
13  4k 
13  4k   
k 1 
13
13




 a2

0

B  O
,
2
 m 2

13





x 

The only real part of ak
in Ae gives nonnegligible contribution.
●That term is sensitive
to the mass hierarchy.
2,
●Because of factor 1/k
large k modes is not
important.
●
Fourier modes of the density distribution
Tokai-to-Kamioka case
Tokai-to-Korea case
distribution: symmetric
→ The real parts are large.
Largest coefficient：
[Reρ1]/ρ0 = 1%
Largest coefficient： （L=1000km）
[Reρ1]/ρ0 =-3.3 %
The effect on χ2 analysis
Previous 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.
ρSK 2.8
error 3%→6%
OLD
3+
→2.6g/cm
Δχ2=22.2
+0.6
The difference of the
matter effect gets
large.
-0.6
+ Fourier mode
Total
+0.5
22.7
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
Δχ2=22.2
ρSK 2.8
→2.6g/cm3+
error 3%→6%
+ Fourier mode
Total
+0.6
-0.6
+0.5
22.7
Tokai-to-Kamioka-and-Korea experiment
Down side of the T2K beam
will appear in Korea while the
T2K is running.
→We can operate two LBL
experiments, Tokai-toKamioka and Tokai-to-Korea.
OAB 3.0 @ SK
mass hierarchy and the matter effect in T2KK
The difference of the amplitudes near the
oscillation maximum.
P(| 13 |  )  P e (| 13 |  )  P e (| 13 |  )
Kr
SK
4 sin 2  atm sin 2  rct Kr SK

(a  a )
2
m13
Significance to the mass hierarchy pattern
(rough estimation)
 P(13  0)  P(13  0) 

  
 (P)


2
2
2
 4 sin 2  atm sin 2  rct  Kr
SK 2

 
(
a

a
)
2

 m13 (P)

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.