1. Constraint on  13 from the Super- Kamiokande atmospheric neutrino data Kimihiro Okumura (ICRR) for the Super-Kamiokande collaboration December 9, 2004 RCCN workshop @ Kashiwa ICRR

2. Outline In this talk, 3-flavor oscillation analysis results, assuming one mass scale dominance (  m 12 2 =0), will be presented. We will have two more talks on:  Effect of solar oscillation term (  m 12 2 ≠0 ) in atmospheric neutrino sample  Future possibilities M. Shiozawa’s talk S. Nakayama’s talk

3. Observation of Atmospheric Neutrinos in Super- Kamiokande Fully Contained (E ~1GeV, e  ) Stopping  (E  ~10GeV,  ) Partially Contained (E ~10GeV,  ) Through-going  (E  ~100GeV,  ) 1000 m underground 50,000 ton (22,500 ton fid.) 11,146 20 inch PMTs (SK-I) 1,885 anti-counter PMTs Water Cherenkov detector Event classification

4. Neutrino oscillation with  m 12 =0 Neutrino Mixing : Weak eigenstates : Mass eigenstates c ij =cos  ij s ij =sin  ij Mixing Matrix : In the approximation of  m  2 =0 (We know  m 12 2 ~8.3×10 -5 eV 2 ) expressed with three parameters (  m 23 2,  23,  13 )  13 =0 2-flavor oscillation (  ↔  six parameters (  m 12 2,  m 23 2,  12,  23,  13,  ) in case of vacuum oscillation 3-flavor oscillation with  m 12 2 =0 two parameters (  m 23 2,  23 )

5. Search for non-zero  13 Electron appearance expected in the 2 -10GeV upward going events. E (GeV) cos  matter effect vacuum oscillation s 2 13=0.05 s 2 13=0.00 null oscillation Electron appearance 1+multi-ring, e-like, 2.5 - 5 GeV 0.45 Mtonyr (Super-K 20yrs) oscillation w/ matter constraint on  13 given by reacter experiment; sin 2  13 <0.05

6. SuperK-I atmosheric neutrino data special sample: Multi-Ring electron to increase multi-GeV e sensitivity CC e CC  1489day FC+PC + 1646day upward going muon data

7. Selection criteria for Multi-GeV Multi-Rring electrons FC, Evis>1.33GeV Most energetic ring is electron-like Log(electron likelihood) > 0 defined by following variables; 1.PID likelihood 2.Momemtum fraction of most energetic ring 3.Number of decay-electrons 4.Distance btw decay-e and primary vertex considering energy dependence We used Likelihood method to discriminate multi-G multi-R electrons;

8. Total electron-likelihood w/ L cutw/o L cut e CC 73.552.0  CC 11.426.7 NC15.121.3 e CC events are enhanced by Likelihood cut  52% → 74% (percentage %) select

9. Binning for 3flavor analysis single-R muon multi-R muon Up-stop Up-thru All zenith angle is 10bins 37 momentum bins x 10 zenith bins = 370 bins in total multi-R electron single-R electron PC-stop PC-thru 1GeV 10GeV zenith angle 10 bin P

10.  2 definition for 3-flavor analysis  2 was calculated with Poisson probability Effect of systematic error was considered for calculating expectation Systematic error terms were obtained by solving linear equation : M ij ×  j =v j (G.L.Gogli et al. hep-ph/0206162)

11. a.Combined overall normalization relative norm. FC/PC relative norm. upstop/upthru b.Neutrino flux  / e below 5GeV  / e above 5GeV anti- e/ e below 10GeV anti- e/ e above 10GeV anti-  /  below 10GeV anti-  /  above 10GeV UP/DOWN ratio Horizontal-vertical in FC/PC Neutrino flight length Energy spectrum K/pi ratio Sample-by-sample normalization (FC multi-GeV  ) Sample-by-sample normalization (PC and upstop) c.Neutrino interactions QE Single-  production DIS DIS Bodek Coherent  production NC/CC Low energy QE Axial vector mass (M A ) Hadron simulator Nuclear effect d.SK 1.Event selection FC reduction PC reduction Upmu efficiency Upmu 1.6GeV cut Flasher BG Cosmic mu BG 2.Event reconstruction Ring-counting Single-R PID Multi-R PID Energy calibration Up/down asymmetry of energy 3.Others a.Tau 4.3flavor analysis Upthru BG in horizontal bin Upstop BG in horizontal bin Non eCC in multi-G single-R electron Non eCC in multi-G multi-R electron Normalization of multi-R electron List of systematic errors Total number of errors: 44

12. Analysis details 100yr Monte Carlo data was generated for expectation 4 step constant function was used for matter density in Earth Averaging technique of oscillation probability was used to compensate small MC statistics  2 was calculated in oscillation parameter space of (  m 2, sin 2  23, sin 2  13 ) Log10(E GeV) P( e  ) P( e  e) Earth radius (km) Matter density averaged  m 2 =2.0x10 -3 eV 2 sin 2  23 =0.5 sin 2  13 =0.05 cos  zenith =-0.6

13. Best-fit zenith angle distributions Null oscillation  2 min /ndf = 376.82/368 @(2.5x10 -3, 0.5, 0.0) CC e CC 

14. multi-GeV electrons UP/DOWN asymmetryZenith angle No significant excess due to matter effect was seen in upward-going multi-GeV electron sample single-R electron multi-R electron

15. Allowed region by 3 flavor analysis  2 min /ndf = 376.82/368 @(2.5x10 -3, 0.5, 0.0) sin 2   sin 2   Normal hierarchy sin 2  13 <0.14 was allowed in 90% C.L. with SK data only

16. Allowed region by 3 flavor analysis sin 2   sin 2    m 2 (eV 2 ) Normal hierarchy 0.36<sin 2  23 <0.65 was allowed in 90% C.L.

17. Normal (  m 2 >0) or inverse (  m 2 <0) mass hierarchy ? Matter effect is different btwn normal / inverse mass hierarchy: Basically, water Cherenkov detector cannot discriminate neutrino/anti-neutrino event-by-event basis, but small effect can be obtained in multi-GeV electron sample due to the difference of cross section, etc.. 3 2 1 3 2 1  m 2 >0  m 2 <0 NormalInverse neutrinoanti-neutrino  m 2 >0 enhancedsuppressed  m 2 <0 suppressedenhanced

18. Normal vs Inverse hierarchy Normal (  m 2 >0) Inverse (  m 2 <0)  2 min /ndf = 376.82/368 @(2.5x10 -3, 0.5, 0.0)  2 min /ndf = 376.76/368 @(2.5x10 -3, 0.525, 0.00625)

19. Summary 3-flavor oscillation analysis with  m 12 2 =0 assumption was performed using SK-I combined (FC+PC+Up  ) dataset. No significance excess in upward-going multi-GeV electron was seen With this oscillation scheme and normal hierarchy assumption, 90% C.L. allowed region was obtained ;  sin 2  13 <0.14  0.36<sin 2  23 <0.65 Both normal and inverse mass hierarchy hypothesis are consistent with Super-K data

20. End