1. Mark Dorman UCL/RAL Hough Methods In The CC Analysis Of The Far Detector Mark Dorman Inclusion of Hough variables into PAN NC/CC discriminating power Obtaining a pure and efficient FD CC sample 1

2. Mark Dorman UCL/RAL Methodology The Hough transform provides a way of quantifying the 'trackiness' or 'showeriness' of an event. I have used (z,tpos) from the SR ntpStrip objects as the 2D input space for the transform. For each strip hit I consider 40 sample gradients from -1.0 to 1.0, calculate intercepts with 'z=0' and then fill Hough space accordingly. I use the reconstructed vertex information to restrict the transform: After Hough space is filled the bin with the highest Hough count is found. Then any bin that has 75% of this highest Hough count contributes towards the RMS75 variables. I assume that the hit with the lowest z-coordinate is the vertex of the event. This is my 'z=0' value for the event. I then require that for any line considered by the transform the transverse position of the line at 'z=0' is not more than 0.5m away relative to the transverse position of the 'z=0' hit. 2

3. Mark Dorman UCL/RAL Hough Variables Used With PAN I add several variables to PAN. Firstly URMS75 and VRMS75. These are the RMS values of the positions in Hough space of the bins with 75% of the highest Hough count relative to this highest bin for the U and V planes respectively. The RMS75 variables are a measure of the localization of a peak in Hough space. A low value indicates high 'trackiness' and a high value indicates high 'showeriness'. I also include the Hough count of the peak bin for the U and V planes. A high value indicates high 'trackiness' and a low value high 'showeriness'. 3

4. Mark Dorman UCL/RAL Files And Cuts I have used the following MDC files: And the following fiducial cuts: Of the ~84K events ~38K pass the fiducial cuts. 4 f24100001_0000.sntp.R1.12.root -> f24100020_0000.sntp.R1.12.root 1m < reco_vtxz < 14m or 17m < reco_vtxz < 28m (track in either supermodule) exclude vertices with transverse position within 0.25m of the centre of the coil hole exclude vertices with transverse position beyond 3.50m of the centre of the coil hole

5. Mark Dorman UCL/RAL RMS75 Variables For CC Events 5 The majority of true CC events have RMS75 values <10.

6. Mark Dorman UCL/RAL RMS75 Variables For NC Events 6 The majority of true NC events have RMS75 values >10.

7. Mark Dorman UCL/RAL Discriminating Power 7 The large number of CC events mean that no direct separation is possible with this variable on it's own.

8. Mark Dorman UCL/RAL Low Energy (<3GeV) Events 8 The situation remains for the low energy events (~8K events after fiducial and true_enu<3 cuts) and the CC distribution is broader.

9. Mark Dorman UCL/RAL Purities And Efficiencies For A CC Sample If all the events that passed the fiducial and energy cut were taken to be CC then the sample would have a purity of ~94%. To reach higher purities can first remove obviously CC events with: There are then 2 variables that can offer better purities; Hough count of peak in Hough space and visible energy. 9 Evtlength > 30 | trkqp/trkeqp | > 10

10. Mark Dorman UCL/RAL Obtaining A Purer CC Sample The following plots show these variables for true CC and NC events after the removal of the obviously CC events: The following pages show how the purities and efficiencies of a CC sample vary when I place a cut on these variables (and call everything to the right of this cut CC). 10 Largest Hough count Visible energy

11. Mark Dorman UCL/RAL Peak Hough Count Cut For a cut at a peak Hough count of 5: 11 efficiency = 96.0% purity = 96.2%

12. Mark Dorman UCL/RAL Visible Energy Cut For a cut at a visible energy of 1: 12 efficiency = 96.9% purity = 96.0%

13. Mark Dorman UCL/RAL Further Work Try to improve the discriminating power of the Hough transform RMS75 variables with - tighter restriction on Hough space with reco_vtx - possible 'pairwise' Hough transform to enhance features in Hough space Look at the ND 13