The earth matter effect in T2KK Based on work with K. Hagiwara, N. Ken-ichi Senda Grad. Univ. for Adv. Studies &KEK

Matter effect and mass hierarchy -Why the matter effect is important?- matter effectCP phase The sign of the matter effect term in A e depends on that of δm 2 13 →One detector experiment cannot solve the correlation between sinθ RCT 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)

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/cm 3 (L = 1000km) 3.03g/cm 3 (L = 1200km) error: ±6% ( ～ 0.18g/cm 3 )

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)] average symmetric distributionasymmetric distribution ● The only real part of a k in Ae gives non- negligible contribution. ● That term is sensitive to the mass hierarchy. ● Because of factor 1/k 2, large k modes is not important.

Fourier modes of the density distribution Tokai-to-Kamioka case Tokai-to-Korea case Largest coefficient ： [Reρ 1 ]/ρ 0 = 1% distribution: symmetric → The real parts are large. Largest coefficient ： （ L=1000km ） [Reρ 1 ]/ρ 0 =-3.3 %

The effect on χ 2 analysis Previous work (hep-ph/ ) detector in Korea: 100kt Water cerenkov running time: 5years (5.0×10 21 POT) density: 2.8 g/cm 3 (Tokai-to-Kamioka) 3.0 g/cm 3 (Tokai-to-Korea) error of density: 3% Fourier mode: not included The best combination to determine the neutrino mass hierarchy （ L=1000km ） Δχ 2 = 22.2 We check the effect of changing the conditions for the matter density to the Δχ 2 of this combination. OLD ρ SK 2.8 →2.6g/cm 3+ error 3%→6% + Fourier mode Total Δχ 2 = The difference of the matter effect gets large. Larger error makes the Δχ 2 smaller Fourier mode helps determining the sign of Δ 13

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/cm 3 ± 6% Tokai-to-Korea 3.0 g/cm 3 ± 6% ● We find the Fourier mode along the baseline is important as well as the error to the average matter density: [Re(ρ 1 )/ρ 0 ]: Tokai-to-Kamioka: 1% Tokai-to-Korea: 3.3% ● The effect of the earth matter effect in chi square analysis. OLD ρ SK 2.8 →2.6g/cm 3+ error 3%→6% + Fourier mode Total Δχ 2 =

Tokai-to-Kamioka-and-Korea experiment OAB 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. The difference of the amplitudes near the oscillation maximum. Significance to the mass hierarchy pattern (rough estimation)