1. Far Detector Fiducial Volume Study Andy Blake Cambridge University Thursday December 7 th 2006

2. Overview Andy Blake, Cambridge UniversityFiducial Volume Study, slide 2 Fiducial volume optimization encompasses the following:

3. All Showers Showers <2 GeV Previous study by Andy Culling (see, for example, doc-db #1136). – Studied bias in reconstructed shower energy close to detector edges. – Studied sensitivity to oscillation parameters as function of fiducial cuts. Previous Study [A. Culling] Andy Blake, Cambridge UniversityFiducial Volume Study, slide 3

4. Fiducial Volume Study Andy Blake, Cambridge UniversityFiducial Volume Study, slide 4 Study following four fiducial containment parameters: – radial edge of detector. – front/back plane of detector – coil hole. COIL HOLE radial cut coil cut back Z cutforward Z cut  COIL HOLE SM1SM2 forward Z cutback Z cut N.B: For purposes of this study, same fiducial cuts applied to both super-modules.

5. Fiducial Volume Study Andy Blake, Cambridge UniversityFiducial Volume Study, slide 5 Use “Cedar” beam MC ntuples for this study. – contained interactions (approx. 800 x 10 20 PoTs). – rock interactions (approx. 100 x 10 20 PoTs). Optimize fiducial cuts by studying the following: Track containment – compare tracks from contained and rock  CC interactions. – study bias in reconstructed muon energy close to detector edges. Shower containment – study bias in reconstructed shower energy close to detector edges. – measure visible energy escaping through detector edges. Oscillation sensitivity – vary each of the fiducial parameters in turn. – calculate sensitivity in  m 2 and sin 2 2 .

6. Track Containment: Front Edge Andy Blake, Cambridge UniversityFiducial Volume Study, slide 6 rock  CC events contained  CC events. Rock muons can sneak into the detector: – up to ~10 cm through the detector edge. – up to ~4 planes through the front plane.

7. Track Containment: Back Edge Andy Blake, Cambridge UniversityFiducial Volume Study, slide 7 Bias in reconstructed muon momentum for tracks exiting through end of detector

8. Shower Extent : Transverse Andy Blake, Cambridge UniversityFiducial Volume Study, slide 8 Transverse extent of showers:

9. Shower Extent: Longitudinal Andy Blake, Cambridge UniversityFiducial Volume Study, slide 9 BACKFORWARD Longitudinal extent of showers:

10. Shower Energy Bias Andy Blake, Cambridge UniversityFiducial Volume Study, slide 10 Calculate mean energy bias as function of radial vertex position. – Only use events where vertex is >20 planes from front and back planes. Distance to detector edgeDistance to centre of coil hole

11. Calculate mean energy bias as function of vertex Z position. – Only use events where vertex is >50cm from edge and >40 cm from centre. Distance to back face of detectorDistance to forward face of detector Shower Energy Bias Andy Blake, Cambridge UniversityFiducial Volume Study, slide 11

12. Shower Energy Loss Andy Blake, Cambridge UniversityFiducial Volume Study, slide 12 Create a fake detector edge to study shower containment. – Calculate the proportion of visible energy contained inside the fake detector volume as a function of the position of the visible shower edge.

13. Shower Energy Loss Andy Blake, Cambridge UniversityFiducial Volume Study, slide 13 Distance to detector edge

14. Shower Energy Loss Andy Blake, Cambridge UniversityFiducial Volume Study, slide 14 Distance to forward face of detectorDistance to back face of detector

15. Oscillation Sensitivity Andy Blake, Cambridge UniversityFiducial Volume Study, slide 15 Calculate sensitivity as function of fiducial cuts. – Vary each cut in turn, holding the others constant. Initial Event Selection. – Reconstructed muon track (must pass track fitter). – Use standard PID with cut placed at PID>0.0. Mechanics of Oscillation Fit. – Purely statistical (ignore all systematic errors). – Fit to overall reconstructed neutrino energy spectrum. E (GeV) = [ 0, 30 ] (60 bins) + 1 bin overflow. – Perform oscillation fit on 120 x 120 grid.  m 2 (10 -3 eV 2 ) = [ 1.5, 4.5 ], Sin 2 2  = [ 0.7, 1.0 ]. – True Oscillation Parameters:  m 2 = 3 x 10 -3 eV 2, Sin 2 2  = 1.0. – True Normalization: 2.5 x 10 20 PoTs. – Simulate 20 experiments at each grid point.

16. Oscillation Sensitivity Andy Blake, Cambridge UniversityFiducial Volume Study, slide 16 Input Data. – Use BOTH rock interactions AND contained events. Sensitivity Calculation. – Determine best fit  m 2 along line of sin 2 2  =1.0. Calculate 99% confidence interval in  m 2. – Determine best fit sin 2 2  along line of best fit  m 2. Calculate 99% confidence interval in sin 2 2 . Fiducial cut parameters. Fiducial CutDefaultRange Radial Edge0.3 m0.0 - 1.0 m Coil Hole0.4 m0.0 - 1.0 m Back Face0.5 m0.1 - 1.5 m Forward Face1.5 m0.5 - 5.0 m

17. Oscillation Sensitivity: Radial Cut Andy Blake, Cambridge UniversityFiducial Volume Study, slide 17  m 2 sensitivity (99% confidence)sin 2 2  sensitivity (99% confidence)

18. Oscillation Sensitivity: Coil Cut Andy Blake, Cambridge UniversityFiducial Volume Study, slide 18  m 2 sensitivity (99% confidence)sin 2 2  sensitivity (99% confidence)

19. Oscillation Sensitivity: Back Edge Andy Blake, Cambridge UniversityFiducial Volume Study, slide 19  m 2 sensitivity (99% confidence)sin 2 2  sensitivity (99% confidence)

20. Oscillation Sensitivity: Forward Edge Andy Blake, Cambridge UniversityFiducial Volume Study, slide 20  m 2 sensitivity (99% confidence)sin 2 2  sensitivity (99% confidence)

21. What are the optimal fiducial cuts ? Andy Blake, Cambridge UniversityFiducial Volume Study, slide 21 Radial EdgeCoil HoleBack PlaneForward Plane Track containment >10 cm> 25 cm> 100 cm Shower energy bias > 20 cm> 40 cm> 60 cm Shower energy loss > 20 cm> 10 cm> 80 cm Oscillation sensitivity < 30 cm< 180 cm require minimal contamination from rock muons. mean track momentum bias must be less than 500 MeV. mean shower energy bias must be less than 100 MeV. visible energy loss must be less than 10%. require optimal sensitivity for oscillation parameters. Criteria Optimal?> 20 cm> 40 cm> 25 cm> 100 cm i.e. must not be more than double the bias observed for highly contained events.

22. Energy-Dependent Fiducial Cuts Andy Blake, Cambridge UniversityFiducial Volume Study, slide 22 reco shower energy could relax fiducial cuts for lowest energy showers

23. Energy-Dependent Fiducial Cuts Andy Blake, Cambridge UniversityFiducial Volume Study, slide 23 Various schemes for energy-dependent fiducial cuts. – Shower Edge Cuts Cut on position of shower edge relative to detector edge. Need to define position of shower edge, plus size of cut. – Fiducial Activity Cuts Cut on amount of shower activity close to detector edge. Need to optimize size of edge region, plus allowed charge. – Apply in addition to, or instead of, fixed fiducial cuts? Apply energy-dependent cuts to all events? Just use these cuts to recover events around detector edge? Example: shower edge cut. – Find closest distance of shower to detector edges. – apply cut at  r > 10 cm and  z > 15 cm.

24. Shower Edge Cut Andy Blake, Cambridge UniversityFiducial Volume Study, slide 24 >10 cm (2 strips)>15 cm (2 planes) Distance to forward face of detectorDistance to radial edge of detector

25. Shower Edge Cut Andy Blake, Cambridge UniversityFiducial Volume Study, slide 25 Distance to forward face of detectorDistance to radial edge of detector After edge cut All showers After edge cut All showers

26. Oscillation Sensitivity Plots Andy Blake, Cambridge UniversityFiducial Volume Study, slide 26 Radial Edge Coil Hole Back Face Forward Face (1) Fixed Fiducial Cuts det.edge - evt.vtx > 20 cm> 40 cm> 25 cmdet.edge - evt.vtx > 100 cm (2) Shower Edge Cuts det.edge - evt.vtx > 10 cm OR det.edge - shw.edge > 10 cm > 40 cm> 25 cmdet.edge - shw.edge > 15 cm (2a) = (1) || (2) (1) || (2) (3) Fiducial Activity Cuts det.edge - evt.vtx > 10 cm OR <10% shw.ph 10cm from edge > 40 cm> 25 cm<10% shw.ph 15cm from edge (3a) = (1) || (3) (1) || (3)

27. Oscillation Sensitivity Plots Andy Blake, Cambridge UniversityFiducial Volume Study, slide 27 99% confidence limits (1) Fixed fiducial cuts (2) Shower edge cuts (2a) = (1) || (2) (3) Fiducial activity cuts (3a) = (1) || (3) Confidence limits are Similar in all cases. Fixed fiducial cuts give best sensitivity contour. – but energy-dependent cuts aren’t optimized. Rescuing events around edge of detector makes sensitivity worse. – needs careful optimization to make sensitivity better. Energy-dependent cuts push contour down. true oscillations

28. Summary Andy Blake, Cambridge UniversityFiducial Volume Study, slide 28 Homing in on optimal fiducial cuts. – studies of biases in reconstructed muon and shower energy. – optimization of sensitivity to oscillation parameters. Current results in good agreement with previous study. Future work: – re-do oscillation fits with finer binning and higher statistics. – study optimization of fiducial cuts at supermodule boundary. – study optimization of energy-dependent fiducial cuts.