1. 1 Super-Kamiokande atmospheric neutrinos Results from SK-I atmospheric neutrino analysis including treatment of systematic errors Sensitivity study based on improved statistics Sensitivity study based on improved systematics S. Moriyama For the Super-Kamiokande collaboration 14 th Sep. 2004 @ NOW2004

2. 2 Event classification Fully Contained (E ~1GeV) Through-going  (E  ~100GeV) Stopping  (E  ~10GeV) Partially Contained (E ~10GeV) energy distribution Super-K and atmospheric neutrinos

3. 3 Super-K I data set and 2 flavor oscillation analysis Data set: full SK-I (FC, PC 1489days, up-  1646 days) Improvements: ● Expectation for neutrino flux - Three dimensional (3D) flux calculation -  interaction parameters (tuned by K2K data) ● Treatment of systematic errors in  2 calculation - Identify fundamental origins of systematic errors, decompose ancient systematic errors into them, and treat them as independent (38 error terms).

4. 4 Zenith angle distributions ~15km ~13000km~500km ~13000km ~500km    2-flavor oscillations Best fit (sin 2 2  =1.0,  m 2 =2.1x10 -3 eV 2 ) Null oscillation

5. 5 Up/Down ratio for FC and PC samples U/D ratio has small systematic error for the expectations. Data is consistent with the expectations with  m 2 ~2x10 -3 eV 2 Stop/through, Vertical/horizontal ratios are also consistent with expectations. Important for future high statistics result. Data Expectation

6. 6 New method for sys. err. treatment Method adopted by Fogli et al. (PRD 053010 (2002)) All of the systematic error terms can be decomposed into many fundamental and independent systematic errors. Linearize the  2 definition for the systematic error terms.  minimization of  2 is equivalent to solving a set of linear equations.

7. 7 New chi square definitions  2 =  +   N MC = N MC 0 P(    )(1+  f  ) for each energy bin f: the fractional change in the predicted event rate in the corresponding energy bin due to a variation of the parameter . d    d    38x38 linear equation matrix, easy to find the local minimum. (N data -N MC ) 2  stat. 2   sys 2 18037 38

8. 8 Category of the systematic errors I Fundamental systematic errors: Neutrino flux Neutrino cross sections Event selection reduction, detection efficiency, hadron simulation, background contamination. Event reconstruction Ring separation, particle ID, energy calibration, U/D  of them (38 terms) are evaluated. SK   Will be explained later.

9. 9 Category of the systematic errors II Fundamental systematic errors: Neutrino flux  a. flux absolute normalization free b. flavor ratios (E 5GeV) 3%, 3-10% c.  ratio (E 10GeV ( e,  ))5%, 5-(10,25)% d. Up/down ratio (FC, each sample correlated)0.4- 2.1% (3D calc.) e. Hor.-vertical ratio (FC, each sample correlated) 0.3- 2.8% (3D calc.) f.K/  ratio 20.0% g. Neutrino flight length 10.0% (scale height) h. Energy spectrum 0.05 for Ep>100GeV i. Sample-by-sample normalization 5% (FC multi-GeV, PC+up stop  )

10. 10 Category of the systematic errors III Fundamental systematic errors: Neutrino cross sections  a. M A in quasi-elastic and single-pi 10% in MA b. Quasi elastic scattering (model dependence)1  = Llewellyn- Smith, Oset c. Quasi elastic scattering (cross section) 10% d. single-pion production (cross section) 10% e. multi-pion production (model dependence)1  = w/, w/o Bodek f. multi-pion production (cross section) 5% g. coherent pion production (cross section)30% h. NC/CC ratio 20% i. Nuclear effect in 16 O (mean free path) 30% j. Charged current  int. (cross section) 30%

11. 11    2-flavor oscillations (FC + PC + UP-  ) Full paper will be soon 0.70.80.910.750.850.95 10 -3 10 -2 Oscillation analysis results 99% 90% 68% Best fit: sin 2 2  =1.0  m 2 = 2.1x10 -3 eV 2  2 = 175.2/177 dof 90% C.L. region: sin 2 2  > 0.92 1.5 <  m 2 < 3.4x10 -3 eV 2  m2

12. 12 Allowed region for sub samples 6 sub samples FC 1-ring SubGeV<400MeV/c FC 1-ring SubGeV>400MeV/c FC 1-ring MultiGeV FC multi-ring PC Upmu The allowed parameter regions suggested by those samples are consistent each other. Sub-GeV low Sub-GeV high Multi-GeV PC Multi-ring upmu

13. 13 Sensitivity study based on improved statictics

14. 14 Statistical improvement for (sin 2 2  23,  m 2 ) 113ktonyr (SK5yrs) 450ktonyr (SK20yrs) 1800ktonyr (SK80yrs) True  m 2 =0.0025 True  m 2 =0.0035 True  m 2 = 0.0015 The allowed region will shrink as a function of sqrt(exposure). The sensitivity does not depend strongly on the true oscillation parameter set.  (s 2  23 ) ～ ±5% @90%CL

15. 15 Sensitivity study based on improved systematics

16. 16 What kind of systematic error term determine the sensitivity (2 flavor case)? Because we decomposed the systematic errors into independent errors, we can track down important systematic errors which affect the (sin 2 2  23,  m 2 ) contour. From the four categories, we try to see the sensitivity with several assumptions: 10yrs exposure with (1) remove all the systematic errors (ultimate case) (2) assume no error from flux (largest effect) (3) assume no error from the interaction (4) assume no error from the SK detector side

17. 17 Comparison of sensitivity with different systematic errors 10yr MC Effects are small  statistics is still important. However, flux uncertainty has some effect on the contour. SK error contribution is very small W/O flux errors Only SK errors No error 10yr MC True  m 2 =0.0021

18. 18 Flux uncertainty: effects on combined analysis  e and up/down asymmetry are important for combined analysis. Though they affect the oscillation contour, the effect is very small.

19. 19 Status of SK-II Atmospheric Neutrinos SK-II event - 311.5days data (preliminary) - SK-II data are consistent with SK-I - Clear deficit in upward  Preliminary!

20. 20 Summary 2 flavor analysis: 90% C.L. allowed region 0.92<sin 2 2  23, 1.5x10 -3 eV 2 <  m 2 <3.4 x10 -3 eV 2 All the data can be explained by the neutrino oscillation very well. More statistics   (sin 2 2  23 ),  (  m 2 ) improve as ~sqrt(exposure). In general, systematic errors don ’ t have large effects on the oscillation contours. If we assume 10yr exposure of SK, only the e  ratio and U/D asymmetry are important systematic error for the combined analysis.