Production of atmospheric neutrinosSome early history (Discovery of atmospheric neutrinos, Atmospheric neutrino anomaly)Discovery of neutrino oscillationsStudies of atmospheric neutrino oscillationsSub-dominant oscillations present and future-Takaaki Kajita (ICRR, U.of Tokyo)

IntroductionWe know that neutrinos have mass:ne nm ntn3n2n1ne nm ntn3n2n1q23=458q12=343q13 < 11Small q13 and Dm122

Event statistics in atmospheric neutrino experimentsTK and Y.Totsuka, RMP73, 85 (2001)More than 20,000 now.

Super-Kamiokande: history and planaccidentSK full reconstruction SK-ISK-IISK-IIIK2KtodayT2K

1996 97 98 992000 01 02 03 04 05 06 07 08 092010 11

(Dm2, sin22q)

SK-I+II atmospheric neutrino data CC neCC nmSK-I: hep-ex/0501064 + SK-II 804 daysOsc.No osc.

Estimating the oscillation parametersTransition point (as a function of energy) Dm2Confirmation of non-oscillated fluxAccurate measurement possible due to small syst. in up/down (2% or less)

nmnt 2-flavor oscillation analysis (SK-I + SK-II combined analysis) FC1ringe-likeFCmringe-likeFC1ringm-likeFCmringm-likePCstopPCthruUPstopPlepSub-GeVMulti-GeVCC neCC nm38 event type andmomentum binsx10 zenith bins

380 binsSince various detector related systematic errors are different,SK-I and SK-II data bins are not combined.380 bins for SK-I + 380 bins for SK-II 760 bins in totalUP throughnon-showeringUP throughshoweringEach box has 10 zenith-angle bins

Definition of c2Poisson with systematic errorsNobs : observed number of eventsNexp : expectation from MCei : systematic error termsi: sigma of systematic errorNumber of data binsNumber of syst error termsc2 minimization at each parameter point (Dm2, sin22q, ). Method (c2 version): G.L.Fogli et al., PRD 66, 053010 (2002).

70 systematic error terms (Free parameter) flux absolute normalization Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV ) Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV ) Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV ) Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV ) Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV ) Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV ) Flux; up/down ratio Flux; horizontal/vertical ratio Flux; K/pi ratio Flux; flight length of neutrinos Flux; spectral index of primary cosmic ray above 100GeV Flux; sample-by-sample relative normalization ( FC Multi-GeV ) Flux; sample-by-sample relative normalization ( PC + Up-stop mu ) Solar activity during SK1 Solar activity during SK-II

MA in QE and single-p QE models (Fermi-gas vs. Oset's) QE cross-section Single-meson cross-section DIS models (GRV vs. Bodek's model) DIS cross-section Coherent-p cross-section NC/CC ratio nuclear effect in 16O pion spectrum CC nt cross-section Reduction for FC Reduction for PC Reduction for upward-going muon FC/PC separation Hadron simulation (contamination of NC in 1-ring m-like) Non-n BG ( flasher for e-like ) Non-n BG ( cosmic ray muon for mu-like ) Upward stopping/through-going mu separation Ring separation Particle identification for 1-ring samples Particle identification for multi-ring samples Energy calibration Energy cut for upward stopping muon Up/down symmetry of energy calibration BG subtraction of up through m BG subtraction of up stop m Non-ne contamination for multi-GeV 1-ring electron Non-ne contamination for multi-GeV multi-ring electron Normalization of multi-GeV multi-ring electron PC stop/through separationFlux (16)n interaction (12)Detector, reduction and reconstruction (212)(SK-I+SK-II, independent)

nm nt 2 flavor analysis Best Fit:Dm2 = 2.5 x 10-3 eV2sin2 2q = 1.00c2 = 839.7 / 755 dof (18%)1.9 x 10-3 eV2 < Dm2 < 3.1 x 10-3 eV2sin2 2q > 0.93at 90% CL1489 days (SK-1)+ 804 days (SK-II)PreliminaryDc2 distributions

L/E analysis

L/E analysis oscillation decoherence decay Further evidence for oscillations Strong constraint on oscillation parameters, especially Dm2 Should observe this dip!SK collab. hep-ex/0404034

L/E plot in 1998 SK evidence paperDue to the bad L/E resolution, the dip was completely washed out. (Or neutrinos decay.) Something must be improved.

Selection criteria Events are not used, if:horizontally going events low energy events Select events with high L/E resolution (D(L/E) < 70%)Similar cut for: FC multi-ring m-like, OD stopping PC, and OD through-going PC

L/E distributionMC (no osc.)SK-I+II, FC+PC The oscillation dip is observed.Mostly down-goingMostly up-goingOsc.MC (osc.)

Allowed oscillation parameters from the SK-I+II L/E analysis(preliminary)SK-I+II2.0 x 10-3 eV2 < Dm2 < 2.8 x 10-3 eV2sin2 2q > 0.93at 90% CLConsistent with the zenith-angle analysisSlightly unphysical region (Dc2=0.5)

SK-I+II L/E analysis and non-oscillation modelsOscillation gives the best fit to the data.Decay and decoherence models disfavored by 4.8 and 5.3 s, resp.c2(osc)=83.9/83dofc2(decay)=107.1/83dofc2(decoherence)=112.5/83dof

Oscillation to nt or nsterile ?

Oscillation to nt or nsterile ? m-like data show zenith-angle and energy dependent deficit of events, while e-like data show no such effect.nmnsterile nmnt orPropagationInteractionDifference in P(nmnt) and P(nmnsterile) due to matter effectNeutral current interactionZ

Testing nmnt vs. nmnsterileUp through muonsnmntHigh E PC events (Evis>5GeV)Multi-ring e-like, with Evis >400MeVNeutral current Matter effectnmnsterilenmnsterilenmntnsterilentPure nmnsterile excluded(PRL85,3999 (2000))

Limit on oscillations to nsterilenm(sinxnsterile+cosxnt)If pure nmnt, sin2x=0If pure nmnsterile, sin2x=1SK collab. draft in preparationConsistent with pure nmntSK-1 data

Seach for CC nt events

Search for CC nt events (SK-I)CC nt eventsntntthadrons Many hadrons (But no big difference with other (NC) events) BAD t- likelihood analysis Upward going only GOOD Zenith angle Only 1.0 CC nt FC events/ktonyr

(BG (other n events) 130 ev./ktonyr) hadronsCC nt MC

Selection of nt eventsPre-cuts: E(visible) >1,33GeV, most-energetic ring = e-likeE(visible)Number of ring candidatesMax. distance between primary vertex and the decay-electron vertexSphericity in the lab frameSphericity in the CM frament MCAtm.n MCdata

Likelihood / neural-net distributionsLikelihoodNeural-netDown-going (no nt)

Zenith angle dist. and fit results Likelihood analysisNN analysiscosqzenithnm, ne, & NC backgroundData

scaled t-MCcosqzenithNumber of eventsFitted # of t eventsExpected # of t eventsZero tau neutrino interaction is disfavored at 2.4s.Hep-ex/0607059

13848(stat) +15 / -32(syst)13448(stat) +16 / -27(syst)7826(syst)7827 (syst)

UNO MEMPHYS Hyper-K INO Super-K

Present and future osc. experimentsPresent: Study of dominant oscillation channels Future: Study of sub-dominant oscillations ne nm ntn3n2n1Solar, KamLANDAtmosphericLong baselineq12, Dm122 Known:Unknown: q13 Sign of Dm232or(CP)If q23 p/4, is it >p/4 or

q13

Search for non-zero q13 in atmospheric neutrino experiments(Dm122=0 and vacuum oscillation assumed)Since ne is involved, the matter effect must be taken into account.

Search for non-zero q13 in atmospheric neutrino experimentsElectron appearance in the multi-GeV upward going events. s213=0.05 s213=0.00 null oscillationMC, SK 20yrsElectron appearance1+multi-ring, e-like, 2.5 - 5 GeVcosQ(Dm122=0 and vacuum oscillation assumed)Assuming n3 is the heaviest:

SK-I multi-GeV e-like dataMulti-GeV, single-ring e-likeMulti-GeV, multi-ring e-like(special)No evidence for excess of upward-going e-like events No evidence for non-zero q13

q13 analysis from Super-K-INormalInvertedHep-ex/0604011

c2 distributionsSK-1 If the shape of c2 continues to be like this, (factor 2) more data might constrain q13 at 90%CL. CHOOZ limit

Future sensitivity to non-zero q13 s22q12=0.825 s2q23=0.40 ~ 0.60 s2q13=0.00~0.04 dcp=45o Dm212=8.3e-5 Dm223=+2.5e-3Positive signal for nonzero q13 can be seen if q13 is near the CHOOZ limit and sin2q23 > 0.520yrs SK3s3s for 80yrs SK~4yrs HKsin2q23=0.600.550.500.450.40Approximate CHOOZ limitBut probably after T2K/Nova

Sign of Dm2

Can we discriminate positive and negative Dm2 ? s(total) and ds/dy are different between n and anti-n. If Dm232 is positive, resonance for n If Dm232 is negative, resonance for anti-n+nny=(En-Em)/Ends/dyEn(GeV)SK atm. n MC

Electron appearance for positive and negative Dm2Single-ring e-likeMulti-ring e-like Positive Dm2 Negative Dm2 null oscillationcosQcosQRelatively high anti-ne fractionLower anti-ne fraction. Small (Large) effect for Dm2 0).

c2 difference (true wrong hierarchy)Dm2: fixed, q23: free, q13: freeExposure: 1.8Mtonyr = 80yr SK = 3.3yr HK True= True= Similar sensitivity (sensitive if sin22q13>0.04) reported by INO (PRD 71, 013001 (2005).

Octant of q23

Solar oscillation effect in atmospheric neutrinos ne nm ntn3n2n1So far, Dm122 has been neglected, because Dm122 (8.010-5)

s22q12=0.825 Dm212=8.310-5 Dm223=2.510-3sin2q13=0Atmospheric neutrinos oscillation by (q12, Dm122).Peres & Smirnov NPB 680 (2004) 479Solar term effect to atmospheric n w/o matter effectwith matter effect

Oscillation probability is different between s2q23=0.4 and 0.6 discrimination between q23 >p/4 and

Effect of the solar terms to the sub-GeV m/e ratio (zenith angle dependence)Below 1.3GeVPm , e < 400 MeVPm , e > 400 MeVDm212= 8.3 x 10-5 eV2Dm223= 2.5 x 10-3 eV2sin2 2q12 = 0.82sin2q13=0sin2q23 = 0.6sin2q23 = 0.4sin2q23 = 0.52 flavor (sin22q23=.96)It could be possible to discriminate the octant of q23, if sin2q23 is significantly away from 0.5.

Constraint on sin2q23 with and without the solar termsSolar terms off : best-fit : sin2 q23 = 0.50

Solar terms on :

best-fit : sin2 q23 = 0.52 (sin2 2q23 = 0.9984)w/o solar termsw/ solar terms(preliminary)Still (almost) maximum mixing is most favored.

Future q23 octant determination with the (12) and (13) terms s2q23=0.40 ~ 0.60 s2q13=0.00~0.04 dcp=45oDiscrimination between q23>p/4 and p/4 and 0.04.sin2q23sin2q23sin2q13sin22q23=0.96sin22q23=0.9990%CL90%CLTest pointFit result

q23 octant determination and syst. errorsDm212= 8.3 x 10-5 eV2Dm223= 2.5 x 10-3 eV2sin2 2q12 = 0.82sin2q13=0Pm , e < 400 MeVsin2q23 = 0.6sin2q23 = 0.4sin2q23 = 0.52 flavor (sin22q23=.96)true0.8 Mtonyr = SK 20yr = HK 0.8yrS.Nakayama, RCCN Int. Workshop on sub-dom. Atm. Osc. 2004

Summary of atmospheric neutrino-2Present atmospheric neutrino data are nicely explained by nm nt oscillations.L/E analysis has shown evidence for oscillatory signature.The data are consistent with tau neutrino appearance.So far, no evidence for sub-dominant oscillations. But future atmospheric neutrino experiments are likely to give unique contribution to this field (especially; solar term effect).

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