Takaaki KajitaICRR, Univ. of TokyoWork done with S.Nakayama, Y.Obayashi, K.Okumura, M.Shiozawa NNN05 workshop,Aussois, Savoie, France, April 2005

ne nm ntn3n2n1Solar, KamLANDAtmosphericLong baselineq12, Dm122 mass and mixing parameters: q12, q23, q13, d, Dm122, Dm132(=Dm232)Known:Unknown: q13 Sign of Dm232orCP ?If q23 p/4, is it >p/4 or

OutlineIntroductionsin2q13 ?Sign of Dm232 ?. q23 >p/4 or

Detector and assumption 48m54m250mDetector: Hyper-Kamiokande The performance of the Hyper-K detector is assumed to be identical to Super-K.Fiducial mass = 0.54 Mton

Search for non-zero q13Electron appearance in the multi-GeV upward going events. En(GeV)cosqzenith s213=0.05 s213=0.00 null oscillation0.45 MtonyrElectron appearance1+multi-ring, e-like, 2.5 - 5 GeVMatter effectcosqzenith(Dm122=0 assumed)

Binning for this analysis (= 3flavor analysis in SK)EnSingle-Ring mMulti-Ring mUp-stopUp-through37 momentum bins x 10 zenith bins = 370 bins in totalMulti-Ring eSingle-Ring ePC-stopPC-through10 zenith angle bins for each box.Small number of events per binPoisson statistics to claculate c2 with 44 systematic error termsMulti-GeVSub-GeVCC neCC nm(or slightly smaller number of bins for some analyses)

Statistical significance for non-zero q13450 ktonyr = 0.8yr HK Dm232 ; positive assumed 3s3s3sImportance of s2q23>0.5; S.Pascoli et al., hep-ph/0305152(Dc2 is approximately proportional to the exposure)

Sign of Dm2 ?Single-ring e-likeMulti-ring e-like Positive Dm2 Negative Dm2 null oscillationcosQcosQRelatively high anti-ne fractionRelatively high ne fraction Dm2=0.002eV2 s2q23 = 0.5 s2q13 = 0.05(0.45 Mtonyr)If Dm232 is positive, resonance for neutrinosIf Dm232 is negative, resonance for anti-neutrinos

c2 difference (inverted-normal)Dm2: fixed, q23: free, q13: freeExposure: 1.8Mtonyr (HK = 3.3 yr)3s3s3sTrue= normal mass hierarchy assumed.

c2 difference (normal inverted)Dm2: fixed, q23: free, q13: freeExposure: 1.8Mtonyr (HK =3.3 yr)3s3s3sTrue= inverted mass hierarchy assumed.

q23 >p/4 or

Expected oscillation with solar terms (1) s22q12=0.825 Dm212=8.310-5 Dm223=2.510-3sin2q13=0Because of the LMA solution, atmospheric neutrinos should also oscillate by (q12, Dm122).Peres & Smirnov NPB 680 (2004) 479

Expected oscillation with solar terms (2)In addition, we may have non-zero q13. s22q12=0.825 Dm212=8.310-5 Dm223=2.510-3(always assumed later in this talk)

Effect of the solar term to sub-GeV e-like zenith anglesub-GeV e-likeDm212= 8.3 x 10-5 eV2Dm223= 2.5 x 10-3 eV2sin2 2q12 = 0.82sin2q13=0sin2 q23 = 0.4sin2 q23 = 0.5sin2 q23 = 0.6(Pe :100 ~ 1330 MeV)(Pe :100 ~ 400 MeV)(Pe :400 ~ 1330 MeV)cosqzenithe-like (3 flavor) / e-like (2 flavor full-mixing)(Much smaller and opposite effect for m-like events.) m/e ratio @low energy is useful to discriminate q23>p/4 and

Discrimination between q23 >p/4 and p/4 and p/4 and 0.04.sin2q23sin2q23sin2q13sin22q23=0.96sin22q23=0.9990%CL90%CLTest pointFit result

Effect of dCP in atmospheric neutrino data no osc. with 80yrs stat.error dCP= 45o 135o 225o 315o s22q12=0.825 s2q23=0.5 s2q13=0.04 Dm212=+8.3e-5 Dm223=+2.5e-3Mutli-GeV, multi-ring e-likee-like (3 flavor) / e-like (no-osc)cosqzenithq13 effectCP effect

Sensitivity to dcp1.8 Mtonyr ~ 3.3yrs HKCP phase could be seen if q13 is close to the CHOOZ limit.sin2q13=0.04sin2q13=0.02sin2q13=0.01 s22q12=0.825 s2q23=0.5 s2q13=0.01~0.04 Dm212=+8.3e-5 Dm223=+2.5e-3sin2q130.10.10.1000Test (d, q13) point0 p 2p0 p 2p0 p 2p0 p 2pCP phase d90%CL99%CL

The present Monte Carlo study suggests that the future atmospheric neutrino experiments with very high statistics will be very interesting, if q13 is large enough.For large q13, atmospheric neutrino experiments with > 2 Mtonyr exposure will; discriminate the mass hierarchy discriminate between q23 >p/4 and

End