1. September 10, 2002M. Fechner1 Energy reconstruction in quasi elastic events unfolding physics and detector effects M. Fechner, Ecole Normale Supérieure In collaboration with M. Campanelli Supervised by A. Blondel

2. September 10, 2002M. Fechner2 Introduction Study of low energy Super Beam + water Cherenkov detector Quasi elastic events are dominant (< 1 GeV) and easier to reconstruct than DIS But they require taking into account detector efficiency and nuclear physics effects (Fermi motion, Pauli blocking) Most previous studies rely on counting the number of oscillated events General unfolding method based on the Monte Carlo re weighting technique in order to recover spectral information

3. September 10, 2002M. Fechner3 Neutrino energy reconstruction CC quasi elastic interactions: only the lepton can be observed (proton below Cherenkov threshold) For a target nucleon at rest, neutrino energy can be exactly reconstructed from lepton information only But in the presence of nuclear effects this does not work any more

4. September 10, 2002M. Fechner4 Fast Monte Carlo simulation Two body kinematics Center of mass lepton angle distribution given by in Gaisser et al. (1986) Fermi momentum k F =225 MeV/c (nucleon momentum isotropic in sphere of radius k F ) n p  kFkF

5. September 10, 2002M. Fechner5 Fast Monte Carlo simulation Pauli blocking: outgoing proton momentum p > k F Nuclear potential well: Standard SPL+UNO event rates considered (baseline 130 km i.e. CERN->Fréjus). Detector resolution (from SuperK): Angular resolution:  ~3° (for e and  ) Momentum resolution:  (E  )/E  ~3%  (E e )/E e ~

6. Energy reconstruction Using the above formula for e and  at low energy (< 1.5 GeV) E gen E reconstructed e  Perfect detection Detector resolution only Nuclear effects only All effects included 6

7. Results of the MC simulation 20% average resolution, 5% negative bias Erec-Egen Resolution e  e  7

8. September 10, 2002M. Fechner8 Need for an unfolding method  disappearance Using true energy Using reconstructed energy Oscillation dip invisible Large water Cherenkov illuminated by SPL->Fréjus superbeam 200 kTyear exposure

9. September 10, 2002M. Fechner9 Fitting for oscillation parameters in presence of distorting effects Classical problem in HEP Solution: Monte Carlo reweighting (used previously e.g. at LEP for W mass fits) Principle: Production of a large MC correspondence table between the real quantity (E gen ) and the measured one (E rec ) and approximate each data event with the MC events sufficiently close to it Since only one MC sample is produced, using a given set   of oscillation parameters, events are given a weight according to the ratio of oscillation probabilities

10. September 10, 2002M. Fechner10 The box method 2 sets of data: ‘experimental’ sample (uses SPL spectra) MC sample For each data event: box around measured value. All MC events inside the box are good approximations of the data and used in the likelihood

11. Box reweighting at work Reconstructed distribution MC events in the box reconstructed generated Data event Image of the box weights MC correspondence table

12. September 10, 2002M. Fechner12 Likelihood function Likelihood function with 2 factors, one from the spectral shape (i.e. box method) and the other describing the Poisson probability for the number of events Where  is the weight and  is the oscillation param. set Counting Spectral shape (box method)

13. September 10, 2002M. Fechner13 Comments on the results We have used binned data (20 MeV wide bins): sum over bins rather than events MC sample ~500 times larger than ‘exp.’ sample The method is general and not limited to event reconstruction in water Cherenkov detectors

14. September 10, 2002M. Fechner14 Fits to  m 2 32 Error ~1%Good linearity and precision over the whole relevant range  m 12 = 0 eV 2 sin 2 2  23 =1, sin 2 2  13 =0.05

15. September 10, 2002M. Fechner15 Fitting the atmospheric parameters 2D plots in the plane ‘Counting’ likelihood: large open contours due to correlations ‘Spectral’ likelihood: uses the reweighting method to extract the maximal amount of information from the spectrum Plots  m 23 =2.5 10 -3  m 12 =5.44 10 -5 tan 2  12 =0.4 sin 2 2  23 =0.95 sin 2 2  13 =0.02  =0 Using the parameters

16. Counting Spectral reconstruction Error on  m 2 ~ 0.7 10 -4 eV 2 Error on sin 2 2  ~ 2% Counting +box

17. September 10, 2002M. Fechner17 Precision on  13   does not modify the energy spectrum (in 1rst approximation)  information mostly contained in the number of events, so the reweighting does not improve the measurement of sin 2 2  13 sin 2 2  13  m 2 23  m 23 =2.5 10 -3  m 12 =5.44 10 -5 tan 2  12 =0.4 sin 2 2  23 =0.95 sin 2 2  13 =0.02  =0 Counting only Counting + box

18. September 10, 2002M. Fechner18 Application to CP-violation Same oscillation parameters in MC and ‘experience’ With neutrinos only and 200 kTyear, sin 2 2  13 =0.02,   Need for antineutrinos !  m 23 =2.5 10 -3  m 12 =5.44 10 -5 tan 2  12 =0.4 sin 2 2  23 =0.95 Counting only Counting+box

19. September 10, 2002M. Fechner19 CP-violation: higher statistics 10fold increase: 2000 kTyear, sin 2 2  13 =0.04,  At 3  CL,  but impossible to measure. Counting only Counting + box Neutrinos only !

20. September 10, 2002M. Fechner20 CP-violation: using antineutrinos Neutrinos ‘exp.’ sample : 200 kTyear statistics sin 2 2   =0.02,  Antineutrino ‘exp.’sample : 1000 kTyear stats sin 2 2   =0.02,  MC sample: 600 times larger than ‘exp.’ with: sin 2 2   =0.04,  Likelihood computed with  and  m 23 =2.5 10 -3 eV 2  m 12 =5.44 10 -5 eV 2 tan 2  12 =0.4 sin 2 2  23 =0.95

21. September 10, 2002M. Fechner21 antineutrinos neutrinos If the box method is not used: With the reweighting method: Error on  is ~3 times worse Counting only ~120° ~35° Counting+Box

22. September 10, 2002M. Fechner22 Conclusion Spectral information is essential in a Super Beam experiment Distortion due to detector and nuclear effects is large Necessity of using adequate unfolding technique to recover spectral information MC reweighting method is very general and can unfold any effect provided they are described correctly in the MC Very good precision on main oscillation parameters. Significant improvements in the CP violation sector.