1. Study of neutrino oscillations with ANTARES J. Brunner

2. Method : Use event ratios MC events with oscillations Split into Non-oscillation event rate Oscillation correction Rate of observed events in 2 channels Can be expressed in these terms Analytical calculation of mixing angle for each Δm 2, error propagation (stat&syst) from R Many systematic effects cancel or attenuate for R 2

3. Choose two appropriate channels Single line events lower energy and more vertical Single line events lower energy and more vertical Multi-line events higher energy & more isotropic Multi-line events higher energy & more isotropic Strong effect of oscillations for single line events – marginal for multiline events Strong effect of oscillations for single line events – marginal for multiline events ElevationNeutrino Energy

4. E/L : differences enhanced R1 = 0.82 (with osc/no osc) R1 = 0.82 (with osc/no osc) R3 = 0.97 (with osc/no osc) R3 = 0.97 (with osc/no osc) Fit mixing angle (linear) for each Δm 2 for ratio R1/R3 Fit mixing angle (linear) for each Δm 2 for ratio R1/R3 In practice : R3 supplies flux normalization In practice : R3 supplies flux normalization

5. Track reconstruction Good efficiency down to low energies Good efficiency down to low energies –20 GeV = 100m muon track for oscillation analysis Good rejection of downgoing muons Good rejection of downgoing muons Reliable zenith angle resolution Reliable zenith angle resolution –few degrees Azimuth determination / pointing accuracy Azimuth determination / pointing accuracy –not needed

6. Reconstruction concept

7. 1.Select “hot spots” at each detector string should correspond to point of closest approach of muon track and detector line

8. 2. Add hits from neighboring floors in narrow time window

9. 3. Perform minimization of time/distance/amplitude related function with all selected hit using a simplified geometry  obtain track parameters

10. Recent clean lowE single-line event Close to vertical Good fit No correlated activity in any other line 10

11. Recent clean lowE single-line event Point of closest approach Cannot be atm muon 7 storeys hit 8 storeys high 100m = 20 GeV Total signal: 17 p.e. 11

12. Data sample 4 years of ANTARES data taking 2007-2010 4 years of ANTARES data taking 2007-2010 2007 : 5 lines active 2007 : 5 lines active 2008-2010 : 10,11,12 lines active 2008-2010 : 10,11,12 lines active Use Physics runs which fulfill basic quality criteria Use Physics runs which fulfill basic quality criteria Total active time : 830 days Total active time : 830 days 12

13. Acceptance to Atmospheric nu’s Two MC samples combined Two MC samples combined Trigger and Reconstruction required Trigger and Reconstruction required No quality cuts No quality cuts 13

14. Multi-line event selection Cuts are chosen for extremely high purity against atm  contribution Cuts are chosen for extremely high purity against atm  contribution Final cuts Fit Quality<1.3 && sinθ<-0.15 (8.6º below horizon) Final cuts Fit Quality<1.3 && sinθ<-0.15 (8.6º below horizon) Vary MC input: water parameters & angular DOM acceptance Vary MC input: water parameters & angular DOM acceptance Data/( +  )MC between 0.97 to 0.815 Data/( +  )MC between 0.97 to 0.815 –compatible with flux uncertainty and total detector acceptance tolerance Numbers are for 2008 only here Numbers are for 2008 only here data 491 MC 504 603  MC 1.2 3.5 cut sinθ<-0.15 tchi2<1.3 cut 14

15. Multi-Line Events for Full data set 1518 Event candidates in total 1518 Event candidates in total Neutrino Oscillation: reduce sample by 3.3% Neutrino Oscillation: reduce sample by 3.3% Muon impurity ~1% Muon impurity ~1% MC 14% high for all years within statistical fluctuations MC 14% high for all years within statistical fluctuations Reminder: Absolute normalisation cancels in event ratio Reminder: Absolute normalisation cancels in event ratio Following plots: MC scaled by 0.857 Following plots: MC scaled by 0.857 15

16. Year by Year Fit Quality 16

17. Year by Year Elevation Angles 17

18. Year by Year Number of Used Storeys 18

19. Single Line Event Selection 2007-2010 Nstorey>7 : hard cut to suppress muons Nstorey>7 : hard cut to suppress muons tchi2<0.95 tchi2<0.95 tcosth > 0 (upward going) tcosth > 0 (upward going) 19

20. Single Line Event Selection 2007-2010 Nstorey>7 : hard cut to suppress muons Nstorey>7 : hard cut to suppress muons tchi2<0.95 tchi2<0.95 tcosth > 0 (upward going) tcosth > 0 (upward going) 20

21. Single-Line MC Year by Year Muon impurity ~5% Muon impurity ~5% Neutrino oscillations Neutrino oscillations –18% reduction –Suppression of ~90 events –Corresponds to ~4-sigma effect w.r.t. statistical error (23 events) 21

22. Single Line Event Selection 2007-2010 Elevation angle in log and linear Elevation angle in log and linear 22

23. Systematic error & Selection Stability Method Method –Use both “Test” MC & “average” MC MC 1 : “low count” MC MC 1 : “low count” MC MC 2 : “high count” MC MC 2 : “high count” MC MC m : “average” MC with MC m = (MC 1 + MC 2 )/2 MC m : “average” MC with MC m = (MC 1 + MC 2 )/2 –Consider Multi-Line and Single-Line Selection –Vary Fit quality cut around chosen value –Evaluate ratios X = MC 1 / MC m for various cuts –Evaluate double ratios X ML / X 1L –Systematic error from variations of X ML / X 1L 23

24. Systematic error Single Line Sample Multi Line Sample Fit quality cut varied 24

25. Systematic error Single Line Sample Multi Line Sample Simulated Muon Rates 25

26. Systematic error Single Line Sample Multi Line Sample Simulated Neutrino Rates 26

27. Systematic error Single Line Sample Multi Line Sample Variation w.r.t. average MC 18% between MC 1 & MC 2 9% variation to MC m Very stable against cut variations Very stable between single-line and multi-line sample cancellation of systematics in R confirmed ! 27

28. Systematic error Consider all 25 combinations of single-line and multi-line cuts Consider all 25 combinations of single-line and multi-line cuts Plot double ratio Plot double ratio –X ML / X 1L Distribution well centered around 1 Distribution well centered around 1 Spread totally contained within 3% Spread totally contained within 3% Propose 3% as conservative syst. error Propose 3% as conservative syst. error Ratio of Ratios 25 entries X ML / X 1L 28

29. Results Assuming “standard” oscillations, coherent data/MC ratio of 0.86 Assuming “standard” oscillations, coherent data/MC ratio of 0.86 Larger year-by-year fluctuations for 1L due to smaller statistics Larger year-by-year fluctuations for 1L due to smaller statistics Ok within statistical error Ok within statistical error Single-line events Multi-line events 29 Data R = 472/1518 = 0.311+/-0.019 (stat&syst) MC Non-Osc: R = 636/1837 = 0.346 Non-oscillation hypothesis at 1.8 sigma from measured ratio

30. Results Assuming “standard” oscillations, coherent data/MC ratio of 0.86 Assuming “standard” oscillations, coherent data/MC ratio of 0.86 Larger year-by-year fluctuations for 1L due to smaller statistics Larger year-by-year fluctuations for 1L due to smaller statistics Ok within statistical error Ok within statistical error Single-line events Multi-line events 30 Data R = 472/1518 = 0.311+/-0.019 (stat&syst) MC Non-Osc: R = 636/1837 = 0.346 Non-oscillation hypothesis at 1.8 sigma from measured ratio PRELIMINARY

31. Example result from MC Active time 2007-2010 : 830 days (220 days with 5 lines only) Active time 2007-2010 : 830 days (220 days with 5 lines only) Assumed true values: Δm 2 =2.4 10 -3 eV 2 & max. mixing Assumed true values: Δm 2 =2.4 10 -3 eV 2 & max. mixing Reachable 1-sigma precision in Δm 2 for maximal mixing 33% Reachable 1-sigma precision in Δm 2 for maximal mixing 33% Best fit 1 sigma 90% C.L. 1 sigma  N1/N2 : 5.7%  Δm 2 : 33%

32. Result 1-sigma in Δm 2 for maximal mixing: 1.4-3.0 10 -3 eV 2 1-sigma in Δm 2 for maximal mixing: 1.4-3.0 10 -3 eV 2 Δm 2 =2.2 +/- 0.8 10 -3 eV 2 Δm 2 =2.2 +/- 0.8 10 -3 eV 2 Active time 2007-2010 : 830 days (220 days with 5 lines only) Active time 2007-2010 : 830 days (220 days with 5 lines only) Non-oscillations excluded at 1.8 sigma Non-oscillations excluded at 1.8 sigma  N1/N2 : 6.1%  Δm 2 : 36% 32

33. Result 1-sigma in Δm 2 for maximal mixing: 1.4-3.0 10 -3 eV 2 1-sigma in Δm 2 for maximal mixing: 1.4-3.0 10 -3 eV 2 Δm 2 =2.2 +/- 0.8 10 -3 eV 2 Δm 2 =2.2 +/- 0.8 10 -3 eV 2 Active time 2007-2010 : 830 days (220 days with 5 lines only) Active time 2007-2010 : 830 days (220 days with 5 lines only) Non-oscillations excluded at 1.8 sigma Non-oscillations excluded at 1.8 sigma  N1/N2 : 6.1%  Δm 2 : 36% 33 PRELIMINARY

34. Next steps Go from event ratio to fit of E/L distribution Go from event ratio to fit of E/L distribution Even better: 2-dim grid in E versus L Even better: 2-dim grid in E versus L Further cleaning of low Energy sample from atmospheric muons needed Further cleaning of low Energy sample from atmospheric muons needed 15 30 45 GeV Differential Effect of oscillations well visible Find magic cut to get rid of this

35. Backup

36. Tau Neutrino appearance ? Cascade-like events effectively suppressed Cascade-like events effectively suppressed 17% branching ratio into muons 17% branching ratio into muons Nutau CC cross section much lower Nutau CC cross section much lower Negligible effect for present analysis Negligible effect for present analysis