1. The Earth Matter Effect in the T2KK Experiment Ken-ichi Senda Grad. Univ. for Adv. Studies

2. Present status of neutrino oscillation parameters

3. Tokai-to-Kamioka (T2K) experiment J-PARC (Tokai) Super – Kamiokande (SK) T2K will start at the beginning of 2009. The beam intensity for the T2K experiment is about 100 times as the one for the K2K experiment. (10 21 Proton On Target / yr) Main purpose: observing the ν μ →ν e transition ( ∝ sin 2 θ rct ) Distance 295km

4. Off-axis beam & T2KK experiment narrow0.5GeV ~ 0.7 GeV ２ ° ～３ ° wideMore than 1.0 GeV near the center （～ 0.5° ） Energy range Peak energy In order to observe the oscillation maxima at SK, the neutrino energy should be 0.5GeV ~ 0.7 GeV High energy neutrino produces a lot ot π 0 ’s ⇒ Back Ground to the ν e appearance event Korea If we place the second detector in Korea, we can perform 2 detector Long baseline neutrino experiment, Tokai-to-Kamioka-and-Korea experiment!!

5. Matter effect, CP phase, and mass hierarchy The interaction with electrons in the earth affects the neutrino oscillation. Matter effect → Matter effect Matter effect Contribution of the solar parameter The interaction between neutrino and the electron affects the neutrino oscillation !! The matter effect term in A e is sensitive to the sign of δm 2 13. In Korea (L ~1000km), this term produces the large difference between thenormal(δm 2 13 >0) and Inverted (δm 2 13 <0) hierarchy. The correlated ambiguity beweenn sin 2 θ RCT and δ MNS can be solved by the difference of the matter effect between Kamioka and Korea.

6. Determining the mass hierarchy in T2KK Input: Normal hierarchy Fit: Inverted hierarchy Input sin 2 2θ RCT = 0.10 δ MNS = 0 K.Hagiwara, N. Okamura, and KS (hep-ph/0607255) Detector size: SK 22.5kt Korea 100kt Matter density: SK 2.8 g/cm 3 Korea 3.0 g/cm 3 Exposure time: 5 years Including the expected constraint on θ RCT from the future reactor experiment Best location to dermine the hierarchy Capability of determining the mass hierarchy by Best combination The hierarchy pattern can be constrained at more than 3σ level if sin 2 2θ RCT > 0,05.

7. Input: normal Fit : normal Inverted δ MNS is constrained ± 30° at 1 sigma level. Around small θ RCT region, the allowed regions for the fake hierarchy remain. Measurement of CP phase in T2KK

8. Earth matter effect Previous studies, we assume that the matter density is constant along the baseline, and the average of the density is same for all Tokai-to- Korea baseline. However... Matter density along the baseline is not constant. Neutrinos travel through various matters. Neutrinos go through deeper region when the baseline length becomes longer. So the matter density distribution depends on the baseline length. We need detail studies on the “earth matter effect ” to justify the potential of T2KK experiment.

9. Earth matter profile - average density- averaged density of the path (g/cm 3 ) base-line length depth of crust 3.00 2.992.872.79-2.0km 3.002.992.902.802.79 0.0 km 2.992.932.822.802.79+2.0km 1200km1150km1100km1050km1000km Error : ±0.1 g/cm 3

10. What is the effect of the local dependent matter effect ? Only the cos modes affect the neutrino oscillation. The oscillation phase is not affected..δA term is sensitive to the hierarchy pattern.

11. Earth matter profile - fluctuation-

12. Previous ： ρ=3.0 g/cm 3 New: Earth matter effect The significance to determine the hierarchy at the best point becomes lower. ← The averaged matter effect becomes small ρ=3.0g/cm 3 → 2.8g/cm3 But… We can still confirm the mass hierarchy at more than 4 σ CL!! Capability of the mass determination

13. Summary The lower side of the T2K beam will appear in Korea. The matter effect in T2KK experiment is key to determine the mass hierarchy pattern and CP phase. The mean value of the density along the Tokai-to- Korea baselines are 2.8, 2.9, and 3.0 g/cm 3 for L = 1000, 1100, 1150km, respectively. The only first Fourier mode and the average matter density are important in T2KK experiment. The best combination (SK3.0deg + Korea 0.5 deg.) keep the enough capability to determine the hierarchy, whenever we consider the earth matter distribution along each baseline length.

14. For Achivement 1 st Workshop: November 2005 @ KIAS 2 nd Workshop: July 2006 @Soul National Univ. Topic: The kind of detectors, Candidate place for constructing the detector in Korea Sensitivity to the new physics How to solve the atomospheric-angle degeneracy 3 rd Work shop: September 2007 in Tokyo

15. To Be Continued…….

16. Analysis method Detector size (fiducial volume) Super-Kamiokande : 22.5 kt The detector in Korea : 100 kt Exposure time 5 years ( time of T2K running) → 5 × 10 21 Proton On Target Matter density Tokai-to-Kamioka: 2.8 g/cm 3 Tokai-to-Korea: 2.0 g/cm 3 Base line length and off-axis angle Kamioka: L = 295 km off-axis angle: 2.5°, 3.0° Korea: L = 1000km – 1200km off-axis angle: 0.5°- 3.0 ° Signals Charged Current Quasi Elastic Events … We can reconstruct the neutrino energy and distinghish e events and μ events. bin width: 200MeV 0.4 – 5.0 GeV for  -like (SK/Korea) 0.4 – 1.2 GeV for e-like (SK) 0.4 – 2.8 GeV for e-like (Korea) Background Secondary neutrino flux of the ν μ primary beam.

17. 2222 event numbers systematic errors parameter errors expected Constraint form KASKA

18. Capability to determine the mass hierarchy 3σ: sin 2 2θ RCT > 0.045 (normal hierarchy) or 0.055 (inverted hierarchy) The normal hierarchy can exclude the fake hierarchy more strongly than the inverted hierarchy. → statistical error. Capability strongly depends on CP phase. ← Contribution of the phase shift !

19. Fit CP phase and reactor angle Fitting CP phase is favored around 0 deg. in order to reduce the phase difference. When the input hierarchy is normal (inverted), the fitting reactor angle is larger (smaller) than input reactor angle.

20. In this analysis, the statistical error is dominant. →Δχ 2 is roughly proportional to detector size of the beam flux. Δχ 2 is proportional to the fudicial volume. Only Hyper?-Kamiokande can not determine the mass hierarchy. Constraint from the reactor experiment plays the same role of Kamioka. Constraint on CP phase by the Kamioka is useful. Optimal ratio is 1:11 ~ 2:4 Total fiducial volume: 600kt