1. Takaaki Kajita (ICRR, U.of Tokyo) 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-

3. Introduction We know that neutrinos have mass: e     3 2 1 3 2 1  23 =45±8  12 =34±3  13 < 11 Small  13 and  m 12 2 <<  m 23 2  OK to interpret the present data with 2 flavor oscillation framework: P(    )=1-sin 2 2  ij ・ sin 2 (1.27  m ij 2 ・ L/E) Atmospheric LBL Solar KamLAND Future experiments

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

5. Super-Kamiokande: history and plan 19 96 97 98 99 20 00 01 02 03 04 05 06 07 08 09 20 10 11 accident SK full reconstruc tion SK-ISK-IISK-III K2K today T2K

6. (  m 2, sin 2 2  )

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

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

9.     2-flavor oscillation analysis (SK-I + SK-II combined analysis)     2-flavor oscillation analysis (SK-I + SK-II combined analysis) FC 1ring e-like FC mring e-like FC 1ring -like FC mring -like PC stop PC thru UP stop P lep Sub-GeV Multi-GeV CC e CC  38 event type and momentum bins x 10 zenith bins  380 bins Since various detector related systematic errors are different, SK-I and SK-II data bins are not combined. 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 UP through non-showering UP through showering Each box has 10 zenith-angle bins

10. Poisson with systematic errors N obs : observed number of events N exp : expectation from MC  i : systematic error term  i : sigma of systematic error Definition of  2 Number of data bins Number of syst error terms  2 minimization at each parameter point (  m 2, sin 2 2 , …). Method (  2 version): G.L.Fogli et al., PRD 66, 053010 (2002).

11. 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 ● M A in QE and single-  ● 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-  cross-section ● NC/CC ratio ● nuclear effect in 16 O ● pion spectrum ● CC   cross-section ● Reduction for FC ● Reduction for PC ● Reduction for upward-going muon ● FC/PC separation ● Hadron simulation (contamination of NC in 1-ring  -like) ● Non- BG ( flasher for e-like ) ● Non- 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  ● BG subtraction of up stop  ● Non- e contamination for multi-GeV 1-ring electron ● Non- e contamination for multi-GeV multi-ring electron ● Normalization of multi-GeV multi-ring electron ● PC stop/through separation Flux (16) interaction (12) Detector, reduction and reconstruction (21×2) (SK-I+SK-II, independent) Detector, reduction and reconstruction (21×2) (SK-I+SK-II, independent)

12.     2 flavor analysis     2 flavor analysis Best Fit:m 2 = 2.5 x 10 -3 eV 2 sin 2 2 = 1.00  2 = 839.7 / 755 dof (18%) 1.9 x 10 -3 eV 2 < m 2 < 3.1 x 10 -3 eV 2 sin 2 2 > 0.93at 90% CL 1.9 x 10 -3 eV 2 < m 2 < 3.1 x 10 -3 eV 2 sin 2 2 > 0.93at 90% CL 1489 days (SK-1)+ 804 days (SK-II) Preliminary  2 distributions

13. L/E analysis

14. oscillation decoherence decay  Further evidence for oscillations  Strong constraint on oscillation parameters, especially  m 2  -like multi-GeV + PC Should observe this dip! SK collab. hep-ex/0404034 L/E analysis P  = (cos 2  sin 2  ・ exp(– )) 2 m 22 L E P  = 1 – sin 2 2  ・ (1 – exp(–   )) 2 1 L E

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

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

18. Allowed oscillation parameters from the SK-I+II L/E analysis (preliminary) SK-I+II 2.0 x 10 -3 eV 2 < m 2 < 2.8 x 10 -3 eV 2 sin 2 2 > 0.93at 90% CL 2.0 x 10 -3 eV 2 < m 2 < 2.8 x 10 -3 eV 2 sin 2 2 > 0.93at 90% CL Consistent with the zenith-angle analysis Slightly unphysical region (  2 =0.5)

19. SK-I+II L/E analysis and non-oscillation models (preliminary) SK-I+II Osc. Decay Decoh. Oscillation gives the best fit to the data. Decay and decoherence models disfavored by 4.8 and 5.3 , resp. Oscillation gives the best fit to the data. Decay and decoherence models disfavored by 4.8 and 5.3 , resp. decoherence decay  2 (osc)=83.9/83dof  2 (decay)=107.1/83dof  2 (decoherence)=112.5/83dof

20. Oscillation to  or sterile ?

21.  -like data show zenith-angle and energy dependent deficit of events, while e-like data show no such effect.   sterile    or x x sterile Propagation Interaction Difference in P(    ) and P(   sterile ) due to matter effect Neutral current interaction Z

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

23. Limit on oscillations to sterile   (sin  ・ sterile +cos  ・  ) If pure   , sin 2  =0 If pure   sterile, sin 2  =1 SK collab. draft in preparation Consistent with pure    SK-1 data

24. Seach for CC  events

25. Search for CC  events (SK-I) CC  events    hadrons ● Many hadrons ．．．． (But no big difference with other (NC) events ． ) BAD  - likelihood analysis ● Upward going only GOOD Zenith angle Only ～ 1.0 CC  FC events/kton ・ yr (BG (other events) ～ 130 ev./kton ・ yr) Only ～ 1.0 CC  FC events/kton ・ yr (BG (other events) ～ 130 ev./kton ・ yr) hadrons CC  MC

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

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

28. Zenith angle dist. and fit results Likelihood analysis NN analysis cos  zenith , e, & NC background Dat a scaled  MC cos  zenith Number of events 138±48(stat) +15 / -32(syst)134±48(stat) +16 / -27(syst) 78±26(syst)78±27 (syst) Fitted # of  events Expected # of  events Zero tau neutrino interaction is disfavored at 2.4 . Hep-ex/0607059

29. UNO MEMPHYS Hyper-K INO Super-K

30. Present: Study of dominant oscillation channels Future: Study of sub-dominant oscillations e     3 2 1 Solar, KamLAND Solar, KamLAND Atmospheric Long baseline Atmospheric Long baseline  12,  m 12 2 Known: Unknown:   13 Sign of  m 23 2 or (CP) If  23 ≠  /4, is it >  /4 or <  /4 ?  23, |  m 23 2 |  Future atmospheric exp’s Present and future osc. experiments

31.  13

32. Search for non-zero  13 in atmospheric neutrino experiments (  m 12 2 =0 and vacuum oscillation assumed) Since e is involved, the matter effect must be taken into account. Earth model Simulation Core Mantle

33. Search for non-zero  13 in atmospheric neutrino experiments Electron appearance in the multi-GeV upward going events. s 2 13=0.05 s 2 13=0.00 null oscillation MC, SK 20yrs Electron appearance 1+multi-ring, e-like, 2.5 - 5 GeV cos  E (GeV) cos  Matter effect (  m 12 2 =0 and vacuum oscillation assumed) Assuming 3 is the heaviest:

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  13

35.  13 analysis from Super-K-I Normal Inverted 3 2 1 3 2 1 Hep-ex/0604011

36.  2 distributions SK-1 If the shape of  2 continues to be like this, (factor ～ 2) more data might constrain  13 at 90%CL. CHOOZ limit

37. Future sensitivity to non-zero  13 s 2 2  12 =0.825 s 2  23 =0.40 ~ 0.60 s 2  13 =0.00~0.04  cp=45 o  m 2 12 =8.3e-5  m 2 23 =+2.5e-3 Positive signal for nonzero  13 can be seen if  13 is near the CHOOZ limit and sin 2  23 > 0.5 20yrs SK 33 3  for 80yrs SK ~4yrs HK sin 2  23 =0.60 0.55 0.50 0.45 0.40 Approximate CHOOZ limit But probably after T2K/Nova…

38. Sign of  m 2

39. Can we discriminate positive and negative  m 2 ?  (total) and d  /dy are different between and anti-.  If  m 23 2 is positive, resonance for   If  m 23 2 is negative, resonance for anti- + CC e Others Multi-ring e-like y=(E -E  )/E d  /dy CC e Others 1-ring e-like Fraction E (GeV) SK atm. MC

40. Electron appearance for positive and negative  m 2 Single-ring e-like Multi-ring e-like Positive  m 2 Negative  m 2 null oscillation cos  Relatively high anti- e fraction Lower anti- e fraction. Small (Large) effect for  m 2 0).

41.  2 difference (true – wrong hierarchy)  m 2 : fixed,  23 : free,  13 : free Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK  m 2 : fixed,  23 : free,  13 : free Exposure: 1.8Mtonyr = 80yr SK = 3.3yr HK 33 True= 33 3 2 1 3 2 1 Similar sensitivity (sensitive if sin 2 2  13 >0.04) reported by INO (PRD 71, 013001 (2005).

42. Octant of  23

43. Solar oscillation effect in atmospheric neutrinos e     3 2 1 So far,  m 12 2 has been neglected, because  m 12 2 (8.0×10 -5 ) <<  m 23 2 (2.5×10 -3 )  m 23 2  m 12 2 However, Diameter of the Earth (L) = 12,800km, Typical atmospheric neutrino energy (E) = 1GeV  (L/E) -1 = 8×10 -5 (km/GeV) -1 However, Diameter of the Earth (L) = 12,800km, Typical atmospheric neutrino energy (E) = 1GeV  (L/E) -1 = 8×10 -5 (km/GeV) -1 Solar oscillation terms cannot be neglected ! ●matter effect must be taken into account ●  13 = 0 assumed.

44. s 2 2  12 =0.825  m 2 12 =8.3×10 -5  m 2 23 =2.5×10 -3 sin 2  13 =0 Atmospheric neutrinos oscillation by (  12,  m 12 2 ). Peres & Smirnov NPB 680 (2004) 479 Solar term effect to atmospheric Solar term effect to atmospheric w/o matter effect with matter effect

45. Oscillation probability is different between s 2  23 =0.4 and 0.6  discrimination between  23 >  /4 and <  /4 might be possible by studying low energy atmospheric e and  events. However, due to the cancellation between   e and e  x, the change in the e flux is small. Solar term effect to atmospheric Solar term effect to atmospheric P 2 : 2 transition prob. e    x by m 12 2 P( e  e ) = 1 – P 2 P( e   ) = P(   e ) = cos 2  23 P 2 e flux (osc) = f( e 0 ) ・ (1-P 2 )+f(  0 ) ・ cos 2  23 P 2

46. Effect of the solar terms to the sub-GeV  /e ratio (zenith angle dependence) Below 1.3GeVP , e < 400 MeVP , e > 400 MeV  m 2 12 = 8.3 x 10 -5 eV 2  m 2 23 = 2.5 x 10 -3 eV 2 sin 2 2  12 = 0.82 sin 2  13 =0 (  e) (3 flavor) (  e) (2 flavor full-mixing) sin 2  23 = 0.6 sin 2  23 = 0.4 sin 2  23 = 0.5 2 flavor (sin 2 2  23 =.96) It could be possible to discriminate the octant of  23, if sin 2  23 is significantly away from 0.5.

47. Solar terms off : best-fit : sin 2  23 = 0.50 Solar terms on : best-fit : sin 2  23 = 0.52 (sin 2 2 23 = 0.9984) Constraint on sin 2  23 with and without the solar terms w/o solar terms w/ solar terms (preliminary) Still (almost) maximum mixing is most favored.

48. Future  23 octant determination with the (12) and (13) terms s 2  23 =0.40 ~ 0.60 s 2  13 =0.00~0.04  cp=45 o Discrimination between  23 >  /4 and <  /4 is possible for all  13. 1.8Mtonyr = SK 80 yrs = 3.3 HK yrs Discrimination between  23 >  /4 and 0.04. sin 2  23 sin 2  13 sin 2 2  23 =0.96sin 2 2  23 =0.99 90%CL Test point Fit result

49.  23 octant determination and syst. errors  m 2 12 = 8.3 x 10 -5 eV 2  m 2 23 = 2.5 x 10 -3 eV 2 sin 2 2  12 = 0.82 sin 2  13 =0 P , e < 400 MeV sin 2  23 = 0.6 sin 2  23 = 0.4 sin 2  23 = 0.5 2 flavor (sin 2 2  23 =.96) (  e) (3 flavor) (  e) (2 flavor full-mixing) true 0.8 Mtonyr = SK 20yr = HK 0.8yr S.Nakayama, RCCN Int. Workshop on sub-dom. Atm. Osc. 2004

50. Present atmospheric neutrino data are nicely explained by    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). Summary of atmospheric neutrino-2

51. End