1. T2KK (without reactor) solves 8-fold degeneracy
Hisakazu Minakata
Tokyo Metropolitan University

2. 日韓新時代: We are having new relationship #2
Congratulations for engagement!
July 13-14, 2006
2nd Korean detector WS

3. n oscillation has been seen!SK
MINOS
KamLAND
July 13-14, 2006
2nd Korean detector WS
K2K

4. Seduction to complete understanding
July 13-14, 2006
2nd Korean detector WS

5. Exploring the MNS matrix
na=Uai ni
Atm + accel n =>
<= solar + reactor n
SK atm
solar+KamLAND
July 13-14, 2006
2nd Korean detector WS

6.  mass hierarchy & absolute mass scale
Normal
Inverted
July 13-14, 2006
2nd Korean detector WS

7. T2KK; Tokai-to-Kamioka-Korea identical two detector complex
New message today !
Ishitsuka et al. 05
T2KK (without reactor) solves 8-fold parameter degeneracy
Copyright: Okamura et al.
July 13-14, 2006
2nd Korean detector WS

8. Current design of Hyper-Kamiokande contains 2 tanks !
Why don’t you bring one of the 2 tanks to Korea?
July 13-14, 2006
2nd Korean detector WS

9. Degeneracy; a notorious obstacle
July 13-14, 2006
2nd Korean detector WS

10. A machinery in my talk
Oscillation probability draw ellipse if plotted in bi-P plane
Role played by CP phase  and the matter clearly distinguished
Art work by Adam Para
Two solutions of S232 x
MN JHEP01
July 13-14, 2006
2nd Korean detector WS

11. Cause of the degeneracy; easy to understand
You can draw two ellipses from a point in P-Pbar space
Intrinsic degeneracy
Doubled by the unknown sign of m2
4-fold degeneracy
July 13-14, 2006
2nd Korean detector WS

12. 23 octant degeneracy Pe= sin2213 x s223 Solar m2 on
OY Nufact03
Pe= sin2213 x s223
Solar m2 on
Matter effect on
Altogether, 2 x 2 x 2 = 8-fold degeneracy
July 13-14, 2006
2nd Korean detector WS

13. Structure of intrinsic & sign-m2 degeneracy in (matter) perturbative regime
Intrinsic degeneracy; 
sign(m2)- degeneracy arises because P is approx. invariant under:
m m2

T2K II
MN JHEP01
July 13-14, 2006
2nd Korean detector WS

14. Let us resolve them one by one; intrinsic degeneracy
July 13-14, 2006
2nd Korean detector WS

15. Expected signal, BG and 2
Kajita in NOVE2006
signal
Expected signal, BG and 2 BG
4yrs n + 4yrs anti-n sin22q13=0.1, d=p/2
n and anti-n ×
Kamioka and Korea
5 energy bins
syst. Errors:
5% BG (overall) 5% BG (energy dep.) 5% signal efficiency
July 13-14, 2006
2nd Korean detector WS

16. Spectral information solves intrinsic degeneracy
from 1000 page Ishitsuka file
T2K
T2KK
2 detector method powerful!
SK momentum resolution ~30 MeV at 1 GeV
July 13-14, 2006
2nd Korean detector WS

17. Sign-m2 degeneracy; the difficult one
July 13-14, 2006
2nd Korean detector WS

18. Sign-m2 degeneracy
Resolution of sign-m2 degeneracy requires the matter effect
Requires baseline ~1000 km
2nd detector seems required to go down to sin2213=.02
July 13-14, 2006
2nd Korean detector WS

19. T2K(0.54 Mt) vs. T2KK(0.27+0.27 Mt)   July 13-14, 2006
2nd Korean detector WS

20. It is not quite only the matter effect
T2KK
Korea only
With the same input parameter and Korean detector of 0.54 Mt the sign-m2 degeneracy is NOT completely resolved
2 identical detector method powerful !
July 13-14, 2006
2nd Korean detector WS

21. T2KK can resolve  mass hierarchy with bonus of better CP sensitivity at large 13
thick: 3, thin: 2
July 13-14, 2006
2nd Korean detector WS

22. Sensitive to  because energy dependence is far more dynamic in 2nd oscillation maximum
July 13-14, 2006
2nd Korean detector WS

23. Why so much care for 23 degeneracy?
July 13-14, 2006
2nd Korean detector WS

24. <-> symmetry for maximal 23 and small 13 ?
If  symmetry is the case …
near maximal 23
small 13
In Z2 case, deviation from max 23 > 13
Grimus et al, Ma, Valle … (many many references)
July 13-14, 2006
2nd Korean detector WS

25. How to solve 23 octant degeneracy
Strategy: Look for terms which depend on 23 but not through the form s232 x sin2213
Detect solar m2 term ~c232
Requires very long baseline
well controlled systematic error plus statistics
Powerful at small 13
Combining reactor measurement of 13
Requires great precision in reactor 13 measurement
Powerful at large 13
July 13-14, 2006
2nd Korean detector WS

26. T2KK solves 23 degeneracy!
July 13-14, 2006
2nd Korean detector WS

27. Solar and atm. terms differ in energy dependences
All different in energy dependences !
July 13-14, 2006
2nd Korean detector WS

28. T2KK in-situ solves 23 octant degeneracy
Kajita et al. to appear See Nakayama-san’s talk for more details
From Nakayama file
July 13-14, 2006
2nd Korean detector WS

29. Atm ; powerful way for octant degene. T.Kajita@NNN05
July 13-14, 2006
2nd Korean detector WS

30. Reactor + accelerator method
MSYIS 02
Acc-disappearance => s223=0.4 or 0.6
Acc-appearance => s223sin2213 = 0.06
Reactor => sin2213 = 0.1
Solves 23 degeneracy
July 13-14, 2006
2nd Korean detector WS

31. Region of resolved 23 degeneracy
T2K II (4MW+HK) + phase II type reactor
Hiraide et al. (7 samurai)
July 13-14, 2006
2nd Korean detector WS

32. Decoupling between degeneracies
Suppose that you succeeded to solve the particular degeneracy, by forgetting about the remaining ones
It does NOT necessarily mean that the problem is solved
You have to verify that your treatment of degeneracy A is valid irrespective of the presence of degeneracy B
One solution: decoupling between the degeneracies
July 13-14, 2006
2nd Korean detector WS

33. 23 and sign-m2 degeneracy decouple
For example, one can show, to first order in matter effect, the followings:
P(octant) = P(1st octant) - P(2nd) is invariant under the interchange of two sign-m2 degenerate pair
P(hierarchy) = P(m2 +) - P(m2 -) is invariant under the interchange of two 23 octant degenerate pair
in T2K or T2KK setting, the intrinsic degeneracy is resolved by spectrum analysis decouple from the game
July 13-14, 2006
2nd Korean detector WS

34. In a nutshell, 8 fold degeneracy can be resolved by T2KK because ..
intrinsic degeneracy is resolved by spectrum information
sign-m2 degeneracy is solved with matter effect + 2 identical detector comparison
23 octant degeneracy is solved by identifying the solar oscillation effect in T2KK
July 13-14, 2006
2nd Korean detector WS

35. Conclusion
With T2KK setting, we have formulated a concrete strategy for resolving 8 fold parameter degeneracy in situ with consistency maintained by “decoupling”
conventional  superbeam can do it !
July 13-14, 2006
2nd Korean detector WS

36. Supplementary slides
July 13-14, 2006
2nd Korean detector WS

37. T2KK vs. NOA; mass hierarchy
thick: 3, thin: 2
NOA: hep-ex/
T2K II
July 13-14, 2006
2nd Korean detector WS

38. T2KK vs. NOA; CP NOA II: hep-ex/0503053 thick: 3 thin: 2
July 13-14, 2006
2nd Korean detector WS