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

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 ?

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

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 = 0.0067 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.

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 ~ 0.65 [ 31 bins ] sin2 2q13 : 0.0015 ~ 0.15 [ 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

Sensitivity study (cont’d) Binning e-like : 5 energy bins (0.4-0.5, 0.5-0.6, 0.6-0.7, 0.7-0.8, 0.8-1.2 GeV) m-like : 20 energy bins (0.2-1.2 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

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) 053010

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.

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

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 .

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/0601258 T2KK has better sensitivity at sin2 2q13 < 0.06~0.07 . sin2 q23

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

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

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.

Supplement

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.