Takaaki Kajita (ICRR, U.of Tokyo)

1. Production of atmospheric neutrinos • Some early history (Discovery of atmospheric neutrinos, Atmospheric neutrino anomaly) • Discovery of neutrino oscillations • Studies of atmospheric neutrino oscillations • Sub-dominant oscillations –present and future- Atmospheric neutrinos Takaaki Kajita (ICRR, U.of Tokyo)

2. Studies of atmospheric neutrino oscillations

3. Introduction We know that neutrinos have mass: Future experiments nenm nt q23=45±8 q13 < 11 q12=34±3 nenm nt n3 n3 Atmospheric LBL n2 Solar KamLAND n2 n1 n1 Small q13 and Dm122 << Dm232 OK to interpret the present data with 2 flavor oscillation framework: P(na nb)=1-sin22qij・sin2(1.27Dmij2・L/E)

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

5. today Super-Kamiokande: history and plan SK-I SK-II SK-III accident SK full reconstruction T2K K2K

6. (Dm2, sin22q)

7. SK-I: 92 kton・yr SK-II: 49 kton・yr Total: 141 kton・yr SK-I+II atmospheric neutrino data CC ne SK-I: hep-ex/0501064 + SK-II 804 days CC nm No osc. Osc.

8. Down-going Up-going Estimating the oscillation parameters Transition point (as a function of energy)  Dm2 Accurate measurement possible due to small syst. in up/down (2% or less) Confirmation of non-oscillated flux

9. nmnt2-flavor oscillation analysis (SK-I + SK-II combined analysis) CC ne CC nm Plep UP through showering FC 1ring e-like FC mring e-like FC 1ring m-like FC mring m-like PC stop PC thru UP through non-showering Multi-GeV UP stop 38 event type and momentum bins x 10 zenith bins  380 bins Sub-GeV Each box has 10 zenith-angle bins Since 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 total

10. Definition of c2 Number of data bins Number of syst error terms Poisson with systematic errors Nobs : observed number of events Nexp : expectation from MC ei : systematic error term si: sigma of systematic error c2 minimization at each parameter point (Dm2, sin22q, …). Method (c2 version): G.L.Fogli et al., PRD 66, 053010 (2002).

11. 70 systematic error terms ● (Free parameter) fluxabsolute 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 ntcross-section Detector, reduction and reconstruction (21×2) (SK-I+SK-II, independent) Flux (16) ●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-necontaminationformulti-GeV 1-ringelectron ●Non-necontaminationformulti-GeV multi-ringelectron ● Normalizationofmulti-GeV multi-ringelectron ● PC stop/through separation ninteraction (12)

12. nm nt2 flavor analysis 1489 days (SK-1)+ 804 days (SK-II) Dc2 distributions Best Fit: Dm2 = 2.5 x 10-3 eV2 sin2 2q = 1.00 c2 = 839.7 / 755 dof (18%) Preliminary 1.9 x 10-3 eV2 < Dm2 < 3.1 x 10-3 eV2 sin2 2q > 0.93 at 90% CL

13. L/E analysis

14. m-like multi-GeV + PC L m Pmm = (cos2q + sin2q ・ exp(– ))2 2t E L 1 Pmm = 1 – sin22q・ (1 – exp(–g0 )) 2 E L/E analysis SK collab. hep-ex/0404034 oscillation decoherence decay Should observe this dip! • Further evidence for oscillations • Strong constraint on oscillation parameters, especially Dm2

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

16. FC single-ring m-like Full oscillation 1/2 oscillation D(L/E)=70% Selection criteria Select events with high L/E resolution (D(L/E) < 70%) Events are not used, if: ★horizontally going events ★low energy events Similar cut for: FC multi-ring m-like, OD stopping PC, and OD through-going PC

17. L/E distribution SK-I+II, FC+PC MC (no osc.) MC (osc.) Mostly down-going Mostly up-going Osc. • The oscillation dip is observed.

18. Allowed oscillation parameters from the SK-I+II L/E analysis SK-I+II (preliminary) Slightly unphysical region (Dc2=0.5) 2.0 x 10-3 eV2 < Dm2 < 2.8 x 10-3 eV2 sin2 2q > 0.93 at 90% CL Consistent with the zenith-angle analysis

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

20. Oscillation to nt or nsterile ?

21. nx nsterile nx 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. nmnt or nmnsterile Difference in P(nmnt) and P(nmnsterile) due to matter effect Propagation Z Neutral current interaction Interaction

22. Testing nmnt vs. nmnsterile Neutral current Matter effect High E PC events (Evis>5GeV) Multi-ring e-like, with Evis >400MeV Up through muons nt nmnsterile nsterile nmnsterile nmnt nmnt (PRL85,3999 (2000)) Pure nmnsterile excluded

23. Limit on oscillations to nsterile nm(sinx・nsterile+cosx・nt) If pure nmnt, sin2x=0 If pure nmnsterile, sin2x=1 SK-1 data Consistent with pure nmnt SK collab. draft in preparation

24. Seach for CC nt events

25. Search for CC nt events (SK-I) CC ntMC CC nt events nt hadrons t nt hadrons ● Many hadrons ．．．． (But no big difference with other (NC) events．) BADt- likelihood analysis ● Upward going only GOOD Zenith angle Only ～ 1.0 CC ntFC events/kton・yr (BG (other n events) ～ 130 ev./kton・yr)

26. Selection of nt events Pre-cuts: E(visible) >1,33GeV, most-energetic ring = e-like Max. distance between primary vertex and the decay-electron vertex E(visible) Number of ring candidates Sphericity in the lab frame nt MC Atm.n MC data Sphericity in the CM frame

27. Up-going Zenith-angle Likelihood / neural-net distributions Down-going (no nt) Likelihood Neural-net

28. Zenith angle dist. and fit results Hep-ex/0607059 Likelihood analysis NN analysis Data scaled t-MC Number of events nm, ne, & NC background cosqzenith cosqzenith Fitted # of t events Expected # of t events Zero tau neutrino interaction is disfavored at2.4s.

29. Sub-dominant oscillations - present and future - Super-K INO MEMPHYS Hyper-K UNO

30. Present and future osc. experiments Present: Study of dominant oscillation channels Future: Study of sub-dominant oscillations Known: Unknown: q12, Dm122 q23, |Dm232| q13 Sign of Dm232 nenmnt n3 or n2 n1 If q23 ≠p/4, is it >p/4 or <p/4 ? (CP) Solar, KamLAND Atmospheric Long baseline  Future atmospheric exp’s

31. q13

32. Earth model Simulation Core Mantle 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.

33. Matter effect cosQ En(GeV) Search for non-zero q13 in atmospheric neutrino experiments (Dm122=0 and vacuum oscillation assumed) MC, SK 20yrs 1+multi-ring, e-like, 2.5 - 5 GeV Assuming n3 is the heaviest: Electron appearance s213=0.05 s213=0.00 null oscillation cosQ Electron appearance in the multi-GeV upward going events.

34. SK-I multi-GeV e-like data Multi-GeV, single-ring e-like Multi-GeV, multi-ring e-like (special) No evidence for excess of upward-going e-like events  No evidence for non-zero q13

35. n2 n3 n1 n2 n3 n1 q13 analysis from Super-K-I Hep-ex/0604011 Normal Inverted

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

37. 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-3 Approximate CHOOZ limit 20yrs SK sin2q23=0.60 0.55 0.50 3s 0.45 0.40 3s for 80yrs SK ~4yrs HK But probably after T2K/Nova… Positive signal for nonzero q13 can be seen if q13 is near the CHOOZ limit and sin2q23 > 0.5

38. Sign of Dm2

39. CC ne CC ne 1-ring e-like Multi-ring e-like Others Others Fraction CC ne CC ne Can we discriminate positive and negative Dm2 ? s(total) and ds/dy are different between nandanti-n. If Dm232 is positive, resonance for n  If Dm232 is negative, resonance for anti-n n + ds/dy n y=(En-Em)/En SK atm. n MC En(GeV)

40. Electron appearance for positive and negative Dm2 Single-ring e-like Multi-ring e-like Relatively high anti-ne fraction Lower anti-ne fraction. Positive Dm2 Negative Dm2 null oscillation cosQ cosQ Small (Large) effect for Dm2 <0 (>0).

41. n2 n3 n1 n2 n3 n1 3s 3s c2 difference (true – wrong hierarchy) Dm2: fixed, q23: free, q13: free Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK True= True= Similar sensitivity (sensitive if sin22q13>0.04) reported by INO (PRD 71, 013001 (2005).

42. Octant of q23

43. Solar oscillation effect in atmospheric neutrinos nenmnt However, Diameter of the Earth (L) = 12,800km, Typical atmospheric neutrino energy (E) = 1GeV  (L/E)-1 = 8×10-5(km/GeV)-1 n3 Dm232 n2 Dm122 n1 So far, Dm122 has been neglected, because Dm122 (8.0×10-5) << Dm232 (2.5×10-3) Solar oscillation terms cannot be neglected ! ●matter effect must be taken into account ●q13 = 0 assumed.

44. Solar term effect to atmospheric n Peres & Smirnov NPB 680 (2004) 479 Atmospheric neutrinos oscillation by (q12, Dm122). s22q12=0.825 Dm212=8.3×10-5 Dm223=2.5×10-3 sin2q13=0 w/o matter effect with matter effect

45. Solar term effect to atmospheric n However, due to the cancellation between nmne and nenx, the change in the ne flux is small. P(ne  ne) = 1 – P2 P(ne  nm) = P(nm  ne) = cos2q23 P2 P2 : 2n transition prob. ne  nxby Dm122 ne flux (osc) = f(ne0)・(1-P2)+f(nm0)・cos2q23P2 Oscillation probability is different between s2q23=0.4 and 0.6 discrimination between q23 >p/4 and <p/4 might be possible by studying low energy atmospheric ne and nm events.

46. (m/e) (3 flavor) (m/e) (2 flavor full-mixing) Effect of the solar terms to the sub-GeV m/e ratio (zenith angle dependence) Dm212 = 8.3 x 10-5 eV2 Dm223 = 2.5 x 10-3 eV2 sin2 2q12 = 0.82 sin2q13=0 Below 1.3GeV Pm , e < 400 MeV Pm , e > 400 MeV sin2q23 = 0.6 2 flavor (sin22q23=.96) sin2q23 = 0.5 sin2q23 = 0.4 It could be possible to discriminate the octant of q23, if sin2q23 is significantly away from 0.5.

47. Constraint on sin2q23 with and without the solar terms Solar terms off : best-fit : sin2 q23 = 0.50 Solar terms on : best-fit : sin2 q23 = 0.52 (sin2 2q23 = 0.9984) w/o solar terms w/ solar terms (preliminary) Still (almost) maximum mixing is most favored.

48. Future q23 octant determination with the (12) and (13) terms s2q23=0.40 ~ 0.60 s2q13=0.00~0.04 dcp=45o 1.8Mtonyr = SK 80 yrs = 3.3 HK yrs 90%CL 90%CL sin22q23=0.96 sin22q23=0.99 Fit result Test point sin2q13 sin2q23 sin2q23 Discrimination between q23>p/4 and <p/4 is possible for all q13. Discrimination between q23>p/4 and <p/4 is marginally possible only for sin2q13 >0.04.

49. (m/e) (3 flavor) (m/e) (2 flavor full-mixing) q23 octant determination and syst. errors S.Nakayama, RCCN Int. Workshop on sub-dom. Atm. Osc. 2004 Dm212 = 8.3 x 10-5 eV2 Dm223 = 2.5 x 10-3 eV2 sin2 2q12 = 0.82 sin2q13=0 0.8 Mtonyr = SK 20yr = HK 0.8yr true Pm , e < 400 MeV sin2q23 = 0.6 2 flavor (sin22q23=.96) sin2q23 = 0.5 sin2q23 = 0.4

50. Summary of atmospheric neutrino-2 • Present 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).