1. CP phase and mass hierarchy Ken-ichi Senda Graduate University for Advanced Studies (SOKENDAI) &KEK This talk is based on K. Hagiwara, N. Okamura, KS PLB 637 266 (2006) (hep-ph/0504061) K. Hagiwara, N. Okamura, KS hep-ph/0607xxx

2. What are the merits of detecting T2K off-axis beam in Korea The term of matter effect at Korea is about 3 times large as one at Kamioka! The term of matter effect is sensitive to the sign of δm 2 13 Contribution of the matter effect

3. Normal hierarchy (Δ 13 > 0): Matter effect enhances the amplitude. Inverted hierarchy (Δ 13 < 0): Matter effect suppresses the amplitude. Near the oscillation maximum (Δ 13 =π) The difference of the amplitudes between at Kamioka and at Korea is very large, and its difference obeys the sign of δm 2 13. Both Kamioka and Korea are important Property of the amplitude

4. The oscillation phase is also sensitive to the sign of Δ 13. sin 2 (|Δ 13 /2| +| Be|) or sin 2 (|Δ 13 /2| - |Be|) Near the oscillation maximum (Δ 13 =π) At Kamioka, the term of cos δ MNS is dominant in B e. ⇒ the sign degeneracy between cos δ MNS and Δ 13 At Korea (L > 1000km), The value of the matter effect term is comparable with the value of cos δ MNS term. ⇒ the sign degeneracy can be solved, but the magnitude of the phase shift strongly depends on the value of cos δ MNS Property of the oscillation phase

5. 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 Base line length and off-axis angle Kamioka: L = 295 km off-axis angle: 3.0° Korea: L = 1000km off-axis angle: 0.5° 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. Contribution from the π 0 is not included.

6. input parameters Solar neutrino –sin 2 2  SOL = 0.84  0.07,  m 12 2 = (8.3  0.6)  10 -5 eV 2 Atmospheric neutrino –sin 2 2  ATM = 0.96-1.00, |  m 13 2 |= (2.5  0.5)  10 -3 eV 2 Matter density （ uncertainty :  3% ） –  = 2.8 / 3.0 (g/cm 3 ) (SK/Korea)

7. 2222 event numbers systematic errors parameter errors expected constraint from future reactor experiments

8. Capability to determine the mass hierarchy 3σ: sin 2 2θ RCT > 0.050 (normal hierarchy) or 0.055 (inverted hierarchy) Normal hierarchy can exclude the fake hierarchy more strongly than the inverted hierarchy. → statistic error. Capability depends on CP phase strongly. ← Contribution of the phase shift ! 3 σ

9. In this analysis, the statistic error is dominant. →Δχ 2 is roughly proportional to the detector sizes and the intensity of the neutrino beam. Δχ 2 is roughly proportional to the volumes. ex.) sin 2 2θ RCT = 0.10 &δ MNS = 0° 22.5kt & 100kt :Δχ 2 ~ 23 100kt & 500kt : Δχ 2 ~ 90 Only Hyper-Kamiokande can not determine the mass hierarchy. The difference between 2 hierarchy patterns is too small at Kamioka. Only Korea is not so bad. The constraint from reactor experiments plays the same role of Kamioka. Optimal ratio is 0.5:5.5 ~ 2:4 Total fiducial volume: 600kt Input:normal Fit: Inverted

10. The mechanism for measuring CP phase and θ RCT Amplitude: sin 2 θ RCT, sin δ MNS 2 detector system: The ambiguity can be solved because of the matter effect. Oscillation phase: cos δ MNS The setup for determination of the mass hierarchy pattern is useful for measurement of CP phase.

11. Input: normal Fit : normal Inverted δ MNS is constrained at least ± 30° at 1 sigma level. In small θ RCT region, the allowed regions for fake hierarchy remain.

12. Input: inverted Fit: Inverted Normal δ MNS is constrained at least ± 30° at 1 sigma level. In small θ RCT region, the allowed regions for fake hierarchy remain.

13. Summary The matter effect is very important for the T2KK experiment. When we detect the off-axis beam 3.0deg by SK and 0.5 deg at L = 1000km by 100kt water cerenkov detector putted in Korea during the T2K experimental period, we can determine the mass hierarchy pattern more than 3 σ C.L!! (sin 2 2θ RCT >0.050 (normal), 0.055 (inverted)) We can also constrain the CP phase uniquely by the same measuring condition without using anti- neutrino beam !

14. To Be Continued…….

15. 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.

16. The importance of ν μ event Without μ event With μ event

17. Importance of μ event –CP phase-

18. Where should we detect the off-axis beam in Korea? 3 σ Input: Normal hierarchy Fit: Inverted hierarchy Input : Inverted Fit : Normal Best combination: OAB3.0° at Kamioka + OAB 0.5° at L = 1000km in Korea 0.5° off-axis beam: flux cover with the oscillation maximum region in Korea (1.6 GeV ~ 2.4 GeV) Input sin 2 2θ RCT = 0.10 δ MNS = 0