T 2 KK solves 8 fold neutrino parameter

T 2 KK solves 8 -fold neutrino parameter degeneracy T. Kajita, *H. Minakata, S. Nakayama, H. Nunokawa November 1, 2006 JPS-APS Joint meeting@Hawaii

T 2 KK; Tokai-to-Kamioka-Korea identical two-detector complex Ishitsuka et al. , hep-ph/0504026 Kajita et al. , hep-ph/0609286 • An improvement over T 2 K II design with Hyper. K @ Kamioka with 1 megaton water November 1, 2006 JPS-APS Joint meeting@Hawaii

T 2 KK; some ongoing activities Korean detector WS 1 st@KIAS (Nov. 05) 2 nd@SNU (July 06), Seoul, Korea November 1, 2006 JPS-APS Joint meeting@Hawaii

Exploring the unknowns; 1 -3 sector and mass hierarchy a=Uai i Atm + accel => <= solar + reactor SK atm November 1, 2006 JPS-APS Joint meeting@Hawaii solar+Kam. LAND

What’s good in T 2 KK? November 1, 2006 JPS-APS Joint meeting@Hawaii

#1. Current design of Hyper. Kamiokande contains 2 tanks ! Why don’t you bring one of the 2 November 1, 2006 tanks to Korea? JPS-APS Joint meeting@Hawaii

#2. Sign- m 2 degeneracy • Resolution of sign- m 2 degeneracy requires the matter effect • Requires baseline ~1000 km • Even for NO A 2 nd detector seems required to go down to sin 22 13=0. 02 November 1, 2006 JPS-APS Joint meeting@Hawaii

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 S 232 x November 1, 2006 HM-H. Nunokawa JPS-APS Joint meeting@Hawaii JHEP 01

#3. Sensitive to because energy dependence is far more dynamic in 2 nd oscillation maximum November 1, 2006 JPS-APS Joint meeting@Hawaii

Spectral information solves degeneracy November 1, 2006 JPS-APS Joint meeting@Hawaii

#4. Sensitive to solar oscillation; good news for 23 octant degeneracy • Detect the effect of the solar term using a far detector in Korea, which has a longer baseline. solar term : electron number density November 1, 2006 : reduced Jarlskog factor JPS-APS Joint meeting@Hawaii

q 23 octant ambiguity P( e) by the solar m 2 is proportional to sin 22 12・cos 2 23 Therefore, it might be possible to measure the octant of 23 by observing the solar oscillation effect in a very long baseline (or very large L/E) experiment. Also S. Nakayama, 2 nd T 2 KK workshop, July 2006, Seoul November 1, 2006 JPS-APS Joint meeting@Hawaii

T 2 KK has two roots 2 detector method; HM-H. Nunokawa, hep-ph/9706281 NO-VE 03@Venice November 1, 2006 JPS-APS Joint meeting@Hawaii

Degeneracy; a notorious obstacle November 1, 2006 JPS-APS Joint meeting@Hawaii

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 m 2 • 4 -fold degeneracy November 1, 2006 JPS-APS Joint meeting@Hawaii

23 octant degeneracy OY Nufact 03 P e= sin 22 13 x s 223 Solar m 2 on Matter effect on Altogether, 2 x 2 = 8 -fold November 1, 2006 JPS-APS Joint meeting@Hawaii degeneracy

factory as ultimate degeneracy solver Typical ‘‘everything at once’’ method • By combining at 3 detectors at 130, 730, and 2810 km, it was claimed that neutrino factory can resolve all the 8 -fold degeneracy if 13 > 1° (Donini, Nu. FACT 03) JPS-APS Joint meeting@Hawaii Powerful, but expensive! ~1000 Million Euro/degeneracy November 1, 2006

Some more advanced comments November 1, 2006 JPS-APS Joint meeting@Hawaii

Spectral information solves intrinsic degeneracy T 2 K from 1000 page Ishitsuka file T 2 KK 2 detector method powerful! SK momentum ~30 Me. V at 1 Ge. V JPS-APSresolution Joint meeting@Hawaii November 1, 2006

Structure of intrinsic & sign- m 2 degeneracy in matter-perturbative regime T 2 K II • Intrinsic degeneracy; • sign( m 2)- degeneracy arises because P is approx. invariant under: • m 2 • MN JHEP 01 November 1, 2006 JPS-APS Joint meeting@Hawaii

T 2 K(0. 54 Mt) vs. T 2 KK(0. 27+0. 27 Mt) November 1, 2006 JPS-APS Joint meeting@Hawaii

It is not quite only the matter effect T 2 KK Korea only • With the same input parameter and Korean detector of 0. 54 Mt the sign- m 2 degeneracy is NOT completely resolved 2 identical detector November 1, 2006 JPS-APS Joint meeting@Hawaii method powerful !

T 2 KK in situ solves 23 degeneracy! November 1, 2006 JPS-APS Joint meeting@Hawaii

Effect of the solar term BG events sin 22 12・cos 2 23 effect visible ○sin 2 23 = 0. 4, sin 2 2 13 = 0. 01 ●sin 2 23 = 0. 6, sin 2 2 13 = 0. 0067 (These parameters are chosen to so that sin 2 23・sin 22 13 is equal. ) m 2: positive = 3/4 Included in this analysis, since 23 is relevant. November 1, 2006 JPS-APS Joint meeting@Hawaii

T 2 KK vs. T 2 K II Comparison hep-ph/0504026 Total mass of the detectors = 0. 54 Mton fid. mass 4 years neutrino beam + 4 years anti-neutrino beam Mass hierarchy 3 (thick) November 1, 2006 CP violation (sin ≠ 0) 2 (thin) JPS-APS Joint meeting@Hawaii

Sensitivity to octant of q 23 OA 2. 5 degree for both Kamioka and Korea sin 22 q 13 sin 22 23=0. 96 sin 22 23=0. 99 2 3 Octant ambiguity of 23 can be resolved if sin 22 23 < ~0. 97 at 2 (almost independent of the value of sin 22 13 and mass hierarchy). November 1, 2006 JPS-APS Joint meeting@Hawaii Can resolve the 8 fold degeneracy of the oscillation parameters.

Sensitivity comparison with T 2 K+Reactor T 2 K-II + phase II reactor sin 2 2 13 T 2 KK Hiraide et al. ; 7 samurai =0 assumed sin 2 2 13 > 3 2~3 November 1, 2006 T 2 KK 2 (rough) hep-ph/0601258 T 2 KK has better sensitivity JPS-APS Joint meeting@Hawaii at sin 2 2 13 < 0. 06~0. 07. 2 sin 23

Expected sensitivity (2) hep-ph/0504026 Total mass of the detectors = 0. 54 Mton fid. mass 4 years neutrino beam + 4 years anti-neutrino beam Mass hierarchy 2 CP violation (sin ≠ 0) 3 2 Kamioka+Korea 3 Kamioka + Korea T 2 K II (Kamioka) November 1, 2006 JPS-APS Joint meeting@Hawaii T 2 K-II (Kamioka)

T 2 KK; points of emphasis • Observing Leptonic CP violation is a challenging goal projects have to be expensive • Sensitivity estimate has to be a reliable one, otherwise … • Restrict to: known background rejection technology by SK + conservative estimate of the systematic errors (5%) + identical 2 detector setting • More aggressive option exists, if you want November 1, 2006 JPS-APS Joint meeting@Hawaii

Signal and BG for various off-axis beams Korea Kamioka 2. 5 degree signal 1. 0 degree By K. Okumura 1. 5 degree signal BG BG sin 2(2 13)=0. 1 =1/2 4 year neutrino run 4 MW beam 2. 0 degree Smaller off-axis angle: Low E BG more serious. (2 nd osc. Max. difficult to see. ) But larger matter effect at the November JPS-APS Joint meeting@Hawaii 1 st osc. Max. . 1, 2006 2. 5 degree

Sensitivity for various OA angles Mass hierarchy CP violation F. Dufour, 2 nd T 2 KK workshop, July 2006, Seoul (Updated) Pre lim Kam only (OA 2. 5) Kam + Korea OA 1. 0 Kam + Korea OA 1. 5 Kam + Korea OA 2. 0 Kam + Korea OA 2. 5 2 3 Mass hierarchy: OA 1. 0 @Korea gives the best sensitivity November 1, 2006 JPS-APS Joint meeting@Hawaii CP violation: Sensitivity depends weekly on the beam option ina ry Could be slightly too optimistic for OA angle less than 2. 5 degrees (The syst errors are assumed to be fully correlated between 2 detectors)

One can resolve degeneracy one by one; decoupling November 1, 2006 JPS-APS Joint meeting@Hawaii

23 and sign- m 2 degeneracy decouple • For example, one can show, to first order in matter effect, the followings: • P(octant) = P(1 st octant) - P(2 nd) is invariant under the interchange of two sign- m 2 degenerate pair • P(hierarchy) = P( m 2 +) - P( m 2 -) is invariant under the interchange of two 23 octant degenerate pair • in T 2 K or T 2 KK setting, the intrinsic degeneracy is resolved by spectrum analysis decouple from the game November 1, 2006 JPS-APS Joint meeting@Hawaii

In a nutshell, 8 fold degeneracy can be resolved by T 2 KK because. . • intrinsic degeneracy is resolved by spectrum information • sign- m 2 degeneracy is solved with matter effect + 2 identical detector comparison • 23 octant degeneracy is solved by identifying the solar oscillation effect in T 2 KK November 1, 2006 JPS-APS Joint meeting@Hawaii

Conclusion • T 2 KK setting has potential of resolving 8 fold parameter degeneracy in situ • Conservative estimate of the sensitivity is given based on known BG rejection technique • Mass hierarchy resolving power can be improved with detector in Korea placed at smaller off-axis angle November 1, 2006 JPS-APS Joint meeting@Hawaii

Nakayama-san’s slide @2 nd Korean detector WS c 2 definition detector x beam e-like bins combination -like bins systematic error term f ij : fractional change in the predicted event rate in the ith bin due to a variation of the parameter e j 2 ej : systematic error parameters, which are varied to minimize c for each chioce of the oscillation parameters November 1, 2006 Approach JPS-APS Joint meeting@Hawaii “ Pull ” G. L. Fogli et al. PRD 66 (2002) 053010