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Update on ND Strip-to-Strip Calibration Work

Update on ND Strip-to-Strip Calibration Work. Mark Dorman Calibration Workshop Fermilab, September 7-9. Introduction and Motivation. My work thus far has involved looking at the ND s2s constants as they exist at the

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Update on ND Strip-to-Strip Calibration Work

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  1. Update on ND Strip-to-Strip Calibration Work Mark Dorman Calibration Workshop Fermilab, September 7-9

  2. 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. 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: • 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 All muon track hits: Rock muon-like sample: • 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 • track is at least 20 planes long • track begins in first 4 planes • event has no showers

  4. 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. 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. 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. Path Length Correction • Hits are then corrected for the path length through scintillator. My correction is basic: • For the 1st track hit I calculate the angle subtended by a line joining it to the • 2nd hit with the z-axis (in 3D). • For the 2nd 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) / cosθz as the path length through scintillator • and hence I just use cosθz 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. 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. 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. Accuracy of the Constants All muon track hits sample for all ND planes using corrected SigLin means. Mean – 0.0063 RMS – 0.0416 All muon track hits sample for all ND planes using corrected SigLin truncated means. Mean – 0.0138 RMS – 0.0358

  11. Accuracy of the Constants All muon track hits sample for calorimeter planes using corrected SigLin means. Mean – -0.0039 RMS – 0.0412 All muon track hits sample for calorimeter planes using corrected SigLin truncated means. Mean – -0.0040 RMS – 0.0354

  12. 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. Errors in Constants (from means) for Calorimeter Errors in Constants (from truncated means) for Calorimeter

  14. 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 / 17001/2) ≈ 0.8%

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