1. T2KK Sensitivity of Resolving q23 Octant Degeneracy
Shoei NAKAYAMA (ICRR, University of Tokyo),
T. Kajita, H. Minakata, and H. Nunokawa
July 13-14, 2006
2nd International Workshop on a Far Detector in Korea for the J-PARC Neutrino Beam
@ SNU, Seoul, Korea

2. Motivation
Planned LBL nm (nm) disappearance measurements can determine sin2 2q23 precisely, but cannot distinguish two possible solutions of sin2 q23 if q23 is not maximal.
If the solar term and higher order terms in sin q13 are neglected, nm(nm)  ne(ne) probability depends on q23 through the form of sin2 2q13 x sin2 q23 . Then, ne (ne) appearance measurements give two degenerate solutions. (sin2 2q13 sin2 q23)1st = (sin2 2q13 sin2 q23)2nd
Accelerator + Reactor could solve this degeneracy in some parameter region (especially at larger sin2 2q13).
Can T2KK solve the q23 octant degeneracy without a help of reactor experiment ?

3. Strategy
Detect the effect of the solar term using a far detector in Korea, which has a longer baseline.
solar term
: electron number density
: reduced Jarlskog factor

4. Effect of the solar term
Dm212 = 8.0 x 10-5 (eV2)
Dm223 = 2.5 x 10-3 (eV2)
sin2 q12 = 0.31
sin22q23 = 0.96
d = 3/4 p
normal mass hierarchy
Effect of the solar term
sin2 q23 = 0.4, sin2 2q13 = 0.01
sin2 q23 = 0.6, sin2 2q13 =
Kamioka 0.27Mton
( 4MW, 4yr n + 4yr n )
Korea 0.27Mton
( 4MW, 4yr n + 4yr n )
Number of signal events
(BG not included)
Solar term is negligibly small
due to shorter baseline in Kamioka.
Solar term can be seen
in low En region in Korea.

5. Sensitivity study Assumption
2.5 o off-axis T2K 4MW beam
4 years n beam + 4 years n beam
Kamioka : 0.27 Mton fid., L = 295 km, r = 2.3 g/cm3 Korea : 0.27 Mton fid., L = 1050 km, r = 2.8 g/cm3
Dm212 = 8.0 x 10-5 (eV2) |Dm223| = 2.5 x 10-3 (eV2) sin2 q12 = 0.31
Oscillation parameter space (unknown parameters)
sin2 q23 : 0.35 ~ [ 31 bins ]
sin2 2q13 : ~ [ 98 bins on log scale ]
dCP : 0 ~ 2p [ 100 bins ]
mass hierarchy : normal or inverted [2 bins ]
 4 dimensional analysis
using no external information on these parameters

6. Sensitivity study (cont’d)
Binning
e-like : 5 energy bins ( , , , , GeV)
m-like : 20 energy bins ( GeV)
(Kamioka, Korea) x (n beam, n beam)
 (5+20) x 4 = 100 bins in total
Systematic errors
e-like bins
BG normalization 5 %
BG spectrum shape 5 % (i-3)/2 (i=1…5 ene bin)
signal normalization 5 %
m-like bins
BG normalization 20 %
spectrum shape 5 % En(GeV)-0.8 / 0.8
both bins
(7) spectrum distortion in Korea shape diff. btw Kam. and Korea  1s

7. c2 definition detector x beam systematic combination error term
e-like bins
m-like bins
f ij : fractional change in the predicted event rate in the ith bin
due to a variation of the parameter e j
j : systematic error parameters, which are varied to minimize c2
for each chioce of the oscillation parameters
“ Pull Approach ” G.L.Fogli et al. PRD66 (2002)

8. An example q23 octant degeneracy solved !!
input answer : sin2 2q13=0.01, d=0.75p
sin2 q23=0.4, normal hierarchy
Kamioka 0.54 Mt
Kamioka 0.27 Mt + Korea 0.27 Mt
sin2 2q13
sin2 2q13
dCP
sin2 q23
q23 octant
degeneracy
solved !!
intrinsic degeneracy
sign-Dm2 degeneracy
q23 octant degeneracy
90 % C.L.
99 % C.L.

9. Sensitivity to q23 octant
sin2 q23=0.38
sin2 q23=0.44
sin2 q23=0.50
sin2 q23=0.56
sin2 q23=0.62
can determine
q23 octant by
> 3s
2~3s

10. Sensitivity to q23 octant (cont’d)
sin2 2q13
sin2 q23
sin2 q23
can determine q23 octant
for any d by
> 3s
2~3s
If sin2 q23<0.42 or >0.58
(sin2 2q23= 0.974), q23 octant
can be determined by >2s
even at very small sin2 2q13 .

11. Sensitivity comparison with T2K+Reactor
d=0 assumed
Sensitivity comparison with T2K+Reactor
T2KK
T2K-II + phase II reactor
sin2 2q13
T2KK 2s
(rough)
> 3s
2~3s
sin2 2q13
hep-ph/
T2KK has better sensitivity
at sin2 2q13 < 0.06~0.07 .
sin2 q23

12. Sensitivity to mass hierarchy (for various q23)
sin2 q23=0.38
sin2 q23=0.44
sin2 q23=0.50
sin2 q23=0.56
sin2 q23=0.62
can determine
mass hierarchy by
> 3s
2~3s
weak dependence
on sin2 q23

13. Sensitivity to leptonic CP violation (for various q23)
sin2 q23=0.38
sin2 q23=0.44
sin2 q23=0.50
sin2 q23=0.56
sin2 q23=0.62
can find
non-zero sin d by
> 3s
2~3s
weak dependence
on sin2 q23

14. Summary
T2KK (Kamioka 0.27 Mton fid. + Korea 0.27 Mton fid., 4 years n run + 4 years n run) can determine q23 octant by itself if sin2 2q23 <0.97 even for very small sin2 2q13 with realistic estimations of systematic errors.

15. Supplement

16. An example input answer : sin2 2q13=0.01, d=0.75p
sin2 q23=0.4, normal hierarchy
Kamioka 0.54 Mt
Korea 0.54 Mt
sin2 2q13
sin2 2q13
dCP
sin2 q23
dCP
sin2 q23
90 % C.L.
99 % C.L.