1. Far Detector Fiducial Volume Studies Andy Blake Cambridge University Saturday February 24 th 2007

2. Overview Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 2 Previous study (doc-db #2467) suggested that the current fiducial volume can be expanded to produce a modest gain in sensitivity, without introducing any significant bias. This talk: – Comparison of sensitivities for current and expanded fiducial volume. – Determination of cosmic muon background. R < √14 m. 0.5 < trk.vtx.z < 14.3 m (SM1). 16.2 < trk.vtx.z < 28.0 m (SM2). R > 0.4 m, R edge > 0.2 m. 4 < trk.vtx.plane < 241 (SM1). 253 < trk.vtx.plane < 466 (SM2). current fiducial volume:expanded fiducial volume:

3. Oscillation Fit Andy Blake, Cambridge UniversityFiducial Volume Study, slide 3 Calculate sensitivity for expanded fiducial volume. – Expand the fiducial volume separately in Z and R. Initial Event Selection. – Reconstructed muon track (must pass track fitter). – Apply PID cut. 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 200 x 200 grid.  m 2 (10 -3 eV 2 ) = [ 2.0, 4.0 ], Sin 2 2  = [ 0.8, 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 100 experiments at each grid point. Use both contained vertex and rock interactions.

4. Expanded Radial Cuts Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 4 Standard Cuts: R < √14 m. New Cuts: >20 cm from edge. >40 cm from coil hole.

5. Expanded Z cuts Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 5 Standard Cuts: 0.5 m < trk.vtx.z < 14.3 m (SM1). 16.2 m < trk.vtx.z < 28.0 m (SM2). New Cuts: 4 < trk.vtx.plane < 241 (SM1). 253 < trk.vtx.plane < 466 (SM2).

6. Comments Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 6 Expanded Radial Cuts. – Gain is small here because standard fiducial cuts are quite tight to begin with (see right). – May gain more with an energy-dependent cut (i.e. expand fiducial volume for clean events). – Should investigate effect of calibration error (and B field error) close to edge of detector. Expanded Longitudinal Cuts. – Standard fiducial cuts are conservative. – Can expand a little in all directions! – Gain is modest, but worth having.

7. Cosmic Muon Background Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 7 Forward-Going CosmicsBackward-Going Cosmics Cosmic muon background divided into forward-going and backward-going events: Background Rejection: Containment Cuts. Track Direction Cuts. (reconstructed as forward-going!) Background Rejection: (Containment Cuts). Track Direction Cuts. Track Timing Cuts.

8. Cosmic Background Determination Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 8 Cosmic muon background determined using “fake” spill triggers. – 3.6M fake triggers from data between May’05 and Feb’06. – Remove LI events, HV trips, coil trips. – Equivalent to 6 mins live time. Compare with MC expectation for cosmic muons. – 50,000 MC cosmic muons processed with Cedar reconstruction. – Equivalent to 19 hrs live time. Compare with MC expectation for beam neutrinos and rock muons. – Normalized to data assuming beam intensity of 2.5e13 PoTs per spill. – Equivalent to 1e20 PoTs. Define: – “Forward-going cosmic” = trk.vtx.y>trk.end.y – “Backward-going cosmic” = trk.vtx.y<trk.end.y

9. Cosmic Background Determination Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 9 Event Selection Cuts: – Reconstructed muon track (must pass track fitter). – Apply PID cut. Containment Cuts: – >20 cm from detector edge. – >40 cm from centre of coil hole. – 4 < vertex plane < 241 (SM1). – 253 < vertex plane < 466 (SM2). Track Direction Cut: – cos θ  > 0.6. (where θ  = reconstructed angle between muon and neutrino). Timing Cut. – Forward timing RMS – Backward timing RMS < 1.66 ns.

10. Forward-Going Cosmics (I) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 10 DISTANCE FROM VERTEX TO EDGE OF DETECTOR

11. Forward-Going Cosmics (II) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 11 DISTANCE FROM VERTEX TO FIRST PLANE OF DETECTOR

12. Forward-Going Cosmics (III) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 12 RECONSTRUCTED ANGLE RELATIVE TO BEAM DIRECTION

13. Backward-Going Cosmics (I) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 13 DISTANCE FROM VERTEX TO EDGE OF DETECTOR

14. Backward-Going Cosmics (II) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 14 RECONSTRUCTED ANGLE RELATIVE TO BEAM DIRECTION

15. Backward-Going Cosmics (III) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 15 FORWARD TIMING RMS – BACKWARD TIMING RMS

16. Results Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 16 MC Beam Neutrinos MC Rock Muons MC Cosmic Muons Data Event Selection200.4 ± 0.5103.4 ± 0.744.8 ± 0.548 Containment Cuts171.1 ± 0.40.5 ± 0.14.3 ± 0.14 Direction Cuts169.5 ± 0.40.3 ± 0.00.7 ± 0.11 Timing Cuts169.4 ± 0.40.3 ± 0.00.1 ± 0.01 Total282.4 ± 0.50.6 ± 0.10.1 ± 0.01 Event Selection134.1 ± 0.460.2 ± 0.652.5 ± 0.767 Containment cuts114.8 ± 0.30.4 ± 0.13.3 ± 0.13 Direction Cuts113.0 ± 0.30.3 ± 0.00.0 ± 0.00 Forward-Going Events (VtxY>EndY): Backward-Going Events (EndY>VtxY):

17. Cosmic Muon Background Results (standard fiducial volume) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 17 MC Beam Neutrinos MC Rock Muons MC Cosmic Muons Data Event Selection200.4 ± 0.5103.4 ± 0.744.8 ± 0.548 Containment Cuts152.0 ± 0.40.3 ± 0.02.7 ± 0.13 Direction Cuts150.7 ± 0.40.3 ± 0.00.6 ± 0.11 Timing Cuts150.6 ± 0.40.3 ± 0.00.1 ± 0.01 Total252.2 ± 0.50.6 ± 0.00.1 ± 0.01 Event Selection134.1 ± 0.460.2 ± 0.652.5 ± 0.767 Containment cuts103.1 ± 0.30.4 ± 0.11.5 ± 0.11 Direction Cuts101.6 ± 0.30.3 ± 0.00.0 ± 0.00 Forward-Going Events (VtxY>EndY): Backward-Going Events (EndY>VtxY):

18. Cosmic Muon Background Event (I) (Run 31373, Snarl 85401) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 18

19. Cosmic Muon Background Event (II) (Run 31373, Snarl 85401) Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 19

20. Summary Andy Blake, Cambridge UniversityFiducial Volume Studies, slide 20 Expanded fiducial volume produces modest gain in sensitivity. – Expanded Z cut produces the larger gain. – Expanded R cut produces a small gain, and needs further study. (e.g. effect of calibration error hasn’t been investigated). Cosmic muon background should be small. – MC expectation is ~0.1 events per 1.0e20 PoTs (1 event observed in data). – No significant increase in background for expanded fiducial volume.