1. Shoei NAKAYAMA (ICRR) for Super-Kamiokande Collaboration December 9, 2004 @ RCCN International Workshop Effect of solar terms to  23 determination in Super-Kamiokande and important systematic errors for future improvements

2. There is no evidence for atmospheric e oscillation. sin 2  13 is consistent with 0 in the present 3 flavor analysis. (  m 2 23, sin 2  23, sin 2  13 ) After solar and KamLAND results, we can say that oscillation of low energy e should appear at some level even if sin 2  13 = 0. (sub-leading oscillations driven by  m 2 12 ) We perform an oscillation analysis taking into account solar parameters (  m 2 12, sin 2 2  12 ) and study their effects. especially in determination of sin 2  23 1. Motivation

3. The analyses in my talk choose sin 2  13 = 0  m 2 12 = 8.3 x 10 -5 eV 2 sin 2 2  12 = 0.83 ( tan 2  12 = 0.41 ) from KamLAND (@ NEUTRINO2004)

4. Oscillation effects in e-like events F osc e = F 0 e P( e  e ) + F 0  P(   e ) F 0 e,F 0   flux w/o osc. = F 0 e [ P( e  e ) + r P(   e ) ] r = F 0   / F 0 e :  /e flux ratio = F 0 e [ 1 – P 2 + r cos 2  23 P 2 ] P 2 = |A e  | 2 : 2 transition probability e   in matter driven by  m 2 12 (F osc e / F 0 e ) – 1 = P 2 ( r cos 2  23 – 1) screening factor for low energy ( r ~ 2 ) ~ 0if cos 2  23 = 0.5 (sin 2  23 = 0.5) 0.5) > 0if cos 2  23 > 0.5 (sin 2  23 < 0.5)

5.  m 2 12 = 8.3 x 10 -5 eV 2 sin 2 2  12 = 0.82, sin 2  13 = 0, sin 2  23 = 0.5 E = 500 MeVcos  = - 0.6 P( e  e ) P(   e )

6. w/o matter effect P(   e ) solar : on sin 2  13 = 0 sin 2  23 = 0.5

7. sub-GeV e-like zenith angle sub-GeV e-like  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  23 = 0.4 sin 2  23 = 0.5 sin 2  23 = 0.6 X : zenith angle Y : N_e (3 flavor) / N_e (2 flavor full-mixing) (P e :100 ~ 1330 MeV)(P e :100 ~ 400 MeV)(P e :400 ~ 1330 MeV)

8. Lepton scattering angle as a function of momentum Low energy leptons have weak angular correlation to the parent direction.

9. sub-GeV e-like momentum sub-GeV e-like  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  23 = 0.4 sin 2  23 = 0.5 sin 2  23 = 0.6 X : electron momentum (MeV/c) Y : N_e (3 flavor) / N_e (2 flavor full-mixing)

10. sub-GeV  -like zenith angle sub-GeV  -like (P  : 200 ~ 1330 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  23 = 0.4 sin 2  23 = 0.5 sin 2  23 = 0.6 2 flavor (sin 2 2  23 = 0.96) X : zenith angle Y : N_  (3 flavor) / N_  (2 flavor full-mixing) (P  : 200 ~ 400 MeV)(P  : 400 ~ 1330 MeV)

11. sub-GeV  /e ratio (zenith angle dependence) sub-GeVP , 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 X : zenith angle Y : R  e (3 flavor) / R  e (2 flavor full-mixing) sin 2  23 = 0.4 sin 2  23 = 0.5 sin 2  23 = 0.6 2 flavor (sin 2 2  23 = 0.96)

12. Oscillation analysis with SK-I data Data set and analysis tools : same as the current standard 3 flavor analysis. Oscillation maps :  m 2 12 = 8.3 x 10 -5 eV 2 sin 2 2  12 = 0.82 sin 2  13 = 0  m 2 23 = 10 -3.2 ~ 10 -2 eV 2 sin 2  23 = 0 ~ 1  2 dimensional analysis Find a  2 min point : projection to the sin 2  23 axis deviation from the 2-3 full mixing ? fixed values from KamLAND same as the standard analysis fixed value

13. Result  2 distribution as a function of sin 2  23 where  m 2 23 is chosen to minimize  2

14. sub-GeV zenith angle distribution

15. sub-GeV  /e ratio (zenith angle dependence)

16. What kind of systematic errors are important for future sin 2  23 determination ? 44 systematic error parameters in the current standard 3 flavor analysis tools. Test with 20yr oscillated MC instead of observed data. ( sin 2  23 = 0.4, 0.45, 0.55, 0.6 and  m 2 23 = 2.5 x 10 -3 eV 2 ) Reduce each systematic error one by one down to ¼ of original

17.  2 distribution with reduced systematic errors true : sin 2  23 = 0.4 Reducing interaction related systematic errors is most important to distinguish sin 2  23 = 0.4 from sin 2  23 = 0.6. Flux errors also give big effects.

18.  2 contribution from sub-samples no change in systematic errors all systematic errors 1/4 Sub-GeV samples play an important role in determination of the sign of the sin 2  23 deviation. (in case of sin 2  13 = 0)

19.  2 distribution for various true sin 2  23 true : sin 2  23 = 0.55 true : sin 2  23 = 0.6true : sin 2  23 = 0.45

20. Which systematic error should be reduced ? (1) Flux sys. errors

21. Which systematic error should be reduced ? (2) Flux, interaction sys. errors interaction sys. errors

22. Which systematic error should be reduced ? (3) interaction sys. errors SK related sys. errors

23. Which systematic error should be reduced ? (4) SK related sys. errors

24. Systematic uncertainties in flux ratios 3 % error for E < 5 GeV flavor ratio anti- / ratios 5 % error for E < 10 GeV

25. Systematic uncertainties in flux up/down ratio P<400MeV/c e-like 0.5% P<400MeV/c  -like 0.8% P>400MeV/c e-like 2.1% P>400MeV/c  -like 1.8%

26. Systematic uncertainties in M A for QE and single-  production models lepton scattering angle R(M A =1.01/M A =1.11) M A = 1.11 M A = 1.01 Sub-GeV single-ring e-like (P e <400MeV/c) Sub-GeV single-ring e-like (P e >400MeV/c) M A = 1.11 M A = 1.01

27. Systematic uncertainties in nuclear effects in QE cross section calculation e e   Neut relativistic Fermi gas model with flat momentum dist. Singh and Oset’s model QE cross section

28. Other important systematic errors primary cosmic ray energy spectral index 0.05 uncertainty ( >100GeV ) NC/CC cross section ratio +- 20 % Nuclear effect in 16 O (absorption, charge exchange, inelastic scattering) +- 30 % Hadron simulation difference between CALOR and FLUKA Energy calibration for FC events +- 2 % 100GeV

29. Reduce 7 dominant systematic errors at once  / e anti- e / e, anti-  /  flux up / down MA in QE, single-  QE cross section model NC / CC ½¼½¼ ½¼½¼ true : sin 2  23 = 0.4true : sin 2  23 = 0.45

30. Summary Effects of solar oscillation parameters on atmospheric oscillations have been studied. Future atmospheric oscillation analysis with 1-2 parameters might provide unique information on the sign of the sin 2  23 deviation (if exists). It’s important to reduce systematic uncertainties on interaction models and flux calculations for low energy (Sub-GeV) neutrinos.

31. Supplement

32. Paolo Lipari @NOON2004

34. Smirnov  m 2 12 = 7.3 x 10 -5 eV 2 sin 2 2  12 = 0.82 P2P2

35. sub-GeV  /e ratio (zenith angle dependence) contd. Sub-GeV (P ,e < 400 MeV/c)Sub-GeV (P ,e > 400 MeV/c)

36. Systematic errors in flux calculations (Up/down asymmetry) HondaFlukaBartoldifference P<400MeV/c e-like 1.0181.0271.024-0.5% (fluka) P<400MeV/c  -like1.0301.0471.038-0.8% (fluka) P>400MeV/c e-like1.0511.0961.059-2.1% (fluka) P>400MeV/c  -like1.0401.0791.051-1.8% (fluka) Multi-GeV e-like0.9971.0280.990-1.5% (fluka) Multi-GeV  -like1.0031.0191.019-0.8% (bartol,fluka) PC0.9951.0050.990-0.5% (fluka) Sub-GeV multi-ring  -like1.0051.0221.008-0.8% (fluka) Multi-GeV multi-ring  -like0.9941.0080.990-0.7% (fluka) Compare Honda2003 flux to Fluka2003 and Bartol2003 flux calculations. Take the difference to be the systematic errors. Predictions of up/down ratio

37. Up-stop Up-through Produced from K Produced from  Fraction of neutrinos produced from K Change the fraction of K by 20%  Systematic error Systematic uncertainties in K/  ratio in flux calculation

38. Systematic uncertainty in primary cosmic ray energy spectrum index e  e  Neutrino flux produced by primary cosmic ray with > 1, 10, 100 1000 GeV Estimate the difference of neutrino flux caused by the E  (>100GeV) in primary spectrum Systematic uncertainty Note: for <100GeV energy spectrum of primary cosmic ray has been measured accurately by BESS and AMS Systematic uncertainty 100GeV

39. Systematic uncertainties in M A for QE and single-  production (angular difference between neutrino and outgoing lepton)  MA=1.01 / MA=1.11 (q 2 correction) Reconstructed  (e)  -like - 251MeV  -like 251 - 400MeV  -like 400 - 630MeV  -like 630 - 1000MeV  -like 1000MeV - e-like - 251MeV e-like 251 - 400MeV e-like 400 - 630MeV e-like 630 - 1000MeV e-like 1000MeV -

40. Systematic uncertainties in nuclear effects in QE cross section calculation e e   Neut relativistic Fermi gas model with flat momentum dist. independent Singh and Oset’s model  (QE) Singh /  (QE) Neut

42. A different point from the current standard 3 flavor analysis Our standard 3 flavor analysis uses an averaging method for the last propagation in mantle. At the present moment, this analysis does not use this averaging method. The 20-neutrino-energies method are used for all MC events.

43. Averaged probability in 3-flavor oscillation Simple in 2-flavor case, but not in 3-flavor case 2-flavor vacuum oscillation : 1-sin 2 2qsin 2 (Dm 2 E/L) → 1-1/2·sin 2 2q due to matter effect and multi-layer density in the earth, oscillation probability is very difficult to be solved analytically We derived averaged transition matrix by following relation: We applied average method for last propagation in the mantle. In the core layers, there is known enhancement by combination of multiple core layers and we don’t take average in the core region. L mantle L mantle

44. Probability calculation recycle MC events to effectively increase MC statistics for each MC event, select 20 MC events with same event type which observed energy is closest to that of original MC event. use 1(original)+20(closest) neutrino energy in calculations of oscillation probability for the original MC event. neutrino production height in the atmosphere updated production height distribution based on HONDA3D calculation 20 probability calculations using 20 neutrino production height, and then take average of the probabilities.