Transcript 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 n i 2 n x L 2k 0 2 Re k cos L k 1 average 2k x Im k sin L symmetric distribution k E ak 7.56 10 5 eV 2 3 g / cm GeV asymmetric distribution P e 4 sin 2 atm sin 2 rct (1 Ae A) sin 2 13 Be B 2 2 2 2 2 Im( ak ) 413 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 atm sin rct Kr SK 2 ( a a ) 2 m13 (P) 2 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. 2