1. Mark Dorman – UCL/RAL – Calibration Workshop Talk Update on ND Strip-to-Strip Calibration Work Mark Dorman Calibration Workshop Fermilab, September 7-9

2. Mark Dorman – UCL/RAL – Calibration Workshop Talk Introduction and Motivation My work thus far has involved looking at the ND s2s constants as they exist at the moment and understanding the various corrections that need to be incorporated to produce them. I decided to try to perform my own quick and dirty s2s calibration as a way to get to grips with the corrections before trying to leverage the work done by Phil. So far I have generated my own constants taking into account the following: I have not yet implemented a 0 or 1 pe correction. I have been working with pME beam MC. The aim of this talk is to quantify how well my constants agree with MC truth as I fold in more of these corrections and then, given the level of this agreement, to look at the constants I produce for real beam data. event and muon track hit pre-selection truncation of strip-end SigLin distributions to remove Landau tail effects attenuation correction (from Calibrator) basic path length through scintillator correction

3. Mark Dorman – UCL/RAL – Calibration Workshop Talk Event and Hit Pre-Selection I have been working with 2 samples – all muon track hits and a rock muon-like track hit sample. My pre-selection criteria are as follows: Shared criteria: All muon track hits: Rock muon-like sample: event has only 1 track track has at least 10 track-like planes difference between track start in U and V views less than 11 planes difference between track end in U and V views less than 6 planes hit path length through scintillator is less than 1.3 cm hit is inside the detector track is at least 20 planes long track begins in first 4 planes event has no showers track is at least 40 planes long if 0 < reco_eshw < 10 GeV remove the first 20 planes from consideration if 10 < reco_eshw < 20 GeV remove the first 30 planes from consideration shower energy less than 20 GeV

4. Mark Dorman – UCL/RAL – Calibration Workshop Talk Event and Hit Pre-Selection The following figures show the effects of the pre-selection criteria on the ‘all hits’ sample: Pre-selection criteria remove about half the hits and the veto region is much more sparsely populated where showers have been removed. The ‘4’ profiles correspond to the 4 plane coverages. The strip-end mean responses are shifted down and the RMS gets lower.

5. Mark Dorman – UCL/RAL – Calibration Workshop Talk Event and Hit Pre-Selection And for the rock muon-like sample: The following pages will always refer to the ‘all hits’ sample due to its larger statistics. Pre-selection criteria remove the vast majority of hits leaving the highest densities in the first planes. Again the strip-end mean responses are shifted down and the RMS gets lower.

6. Mark Dorman – UCL/RAL – Calibration Workshop Talk Attenuation Correction Hits that make it through the pre-selection are corrected for attenuation of the signal along the optical fibres. I am using the mapper data via the Calibrator GetAttenCorrectedTpos() function where the ‘lpos’ argument is taken as the ‘trk.stpu’ value if the hit is in a V plane and vice versa. As such I am just correcting by the same amount as was initially used when the MC was generated (although reconstruction errors can change this): A pictorial representation of the attenuation correction as it exists in the MC for the partially instrumented V planes.

7. Mark Dorman – UCL/RAL – Calibration Workshop Talk Path Length Correction Hits are then corrected for the path length through scintillator. My correction is basic: For the 1 st track hit I calculate the angle subtended by a line joining it to the 2 nd hit with the z-axis (in 3D). For the 2 nd to penultimate hits I calculate the angle subtended by a line joining the hits directly before and after the hit in question with the z-axis. For the last hit on the track I use the angle subtended by a line joining the penultimate hit to the last hit and the z-axis. Geometry then gives 1.0 (cm) / cosθ z as the path length through scintillator and hence I just use cosθ z as the correction factor. Path lengths are mostly close to 1.0 as expected for beam MC. I have only used hits with a path length less than 1.3 cm.

8. Mark Dorman – UCL/RAL – Calibration Workshop Talk Path Length Correction The following plot shows the path length correction in action: The path length correction does a good job of flattening the response up to about 1.3 cm - this is where I have placed a hit pre-selection cut.

9. Mark Dorman – UCL/RAL – Calibration Workshop Talk Deriving the Constants I then use the mean of the mean corrected responses per strip-end to define the value to which all strips will be calibrated. I have employed this methodology to the ‘all track’ and ‘rock muon-like’ samples for all strips in the ND and just in the calorimeter strips (i.e. plane < 121). The following plots show the relative errors in my calculated constants compared to the MC truth for a variety of samples and the colour scheme is as follows: Black – no cuts or corrections Red – pre-selection cuts Blue – pre-selection cuts and path length corrected Pink – pre-selection cuts and attenuation corrected Cyan – all cuts and corrections

10. Mark Dorman – UCL/RAL – Calibration Workshop Talk Accuracy of the Constants All muon track hits sample for all ND planes using corrected SigLin means. All muon track hits sample for all ND planes using corrected SigLin truncated means. Mean – 0.0063 RMS – 0.0416 Mean – 0.0138 RMS – 0.0358

11. Mark Dorman – UCL/RAL – Calibration Workshop Talk Accuracy of the Constants All muon track hits sample for calorimeter planes using corrected SigLin means. All muon track hits sample for calorimeter planes using corrected SigLin truncated means. Mean – -0.0039 RMS – 0.0412 Mean – -0.0040 RMS – 0.0354

12. Mark Dorman – UCL/RAL – Calibration Workshop Talk Accuracy of the Constants It can be seen that the attenuation correction is doing most of the work (as expected) with the pre-selection helping to shift the average responses down towards the truth responses. It can also be seen that truncation of the strip-end response histograms is very useful for reducing the RMS of the errors in the derived constants. I wanted to have some way to quantify how well the corrections and cuts were doing and decided to implement Jeff’s idea of seeing what percentage of strips were more than 2% and 5% wrong. The following slide shows tables of the means and RMS of the error histograms together with these new quantities.

13. Mark Dorman – UCL/RAL – Calibration Workshop Talk Cuts Applied MeanRMS % of constants >2% wrong % of constants >5% wrong None0.00730.099779.250.4 Pre-Select -ion (PS) 0.00210.095780.250.4 PS + Path Length 0.00270.096479.549.5 PS + Atten -uation-0.00390.041251.614.2 All-0.00330.042857.315.3 Cuts Applied MeanRMS % of constants >2% wrong % of constants >5% wrong None0.00210.067370.132.7 Pre-Select -ion (PS) 0.00080.071874.338.2 PS + Path Length 0.00130.071972.935.9 PS + Atten -uation-0.00400.035440.28.8 All-0.00340.036245.08.6 Errors in Constants (from means) for Calorimeter Errors in Constants (from truncated means) for Calorimeter

14. Mark Dorman – UCL/RAL – Calibration Workshop Talk Expected Statistical Error For a typical strip-end in the calorimeter planes: And so the expected error due to statistics is: And so by considering a 3σ deviation (expect ~99% within this) I would expect about 0.4% of strips to be outside 2% wrong due to statistical error. This is clearly not enough to account for the values in the tables on the previous slide. (RMS / mean) ≈ (200 / 630) ≈ 32% # hits in strip ≈ 1700 (32 / 1700 1/2 ) ≈ 0.8%