update on nd strip-to-strip calibration work

Mark Dorman – UCL/RAL – Calibration Workshop Talk

Update on ND Strip-to-Strip Calibration Work

Mark DormanCalibration 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 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


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



• 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 whereshowers 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.



• 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.


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.


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 to1.0 as expected for beam MC. I have only used hits with a path

length less than 1.3 cm.


Path Length Correction

• The following plot shows the path length correction in action:

The path length correctiondoes a good job of flattening

the response up to about 1.3 cm - this is where I have placed a hit pre-selection cut.


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


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 – 0.0063RMS – 0.0416

Mean – 0.0138RMS – 0.0358



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 – -0.0039RMS – 0.0412

Mean – -0.0040RMS – 0.0354



• 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.


Cuts AppliedCuts Applied MeanMean RMSRMS % of % of constants constants

>2% wrong>2% wrong

% of % of constants constants

>5% wrong>5% wrong

NoneNone 0.00730.0073 0.09970.0997 79.279.2 50.450.4

Pre-SelectPre-Select

-ion (PS)-ion (PS)

0.00210.0021 0.09570.0957 80.280.2 50.450.4

PS + Path PS + Path LengthLength

0.00270.0027 0.09640.0964 79.579.5 49.549.5

PS + AttenPS + Atten

-uation-uation-0.0039-0.0039 0.04120.0412 51.651.6 14.214.2

AllAll -0.0033-0.0033 0.04280.0428 57.357.3 15.315.3

Cuts AppliedCuts Applied MeanMean RMSRMS % of % of constants constants

>2% wrong>2% wrong

% of % of constants constants

>5% wrong>5% wrong

NoneNone 0.00210.0021 0.06730.0673 70.170.1 32.732.7

Pre-SelectPre-Select

-ion (PS)-ion (PS)

0.00080.0008 0.07180.0718 74.374.3 38.238.2

PS + Path PS + Path LengthLength

0.00130.0013 0.07190.0719 72.972.9 35.935.9

PS + AttenPS + Atten

-uation-uation-0.0040-0.0040 0.03540.0354 40.240.2 8.88.8

AllAll -0.0034-0.0034 0.03620.0362 45.045.0 8.68.6

Errors in Constants (from means) for Calorimeter

Errors in Constants (from truncated means) for Calorimeter


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%

update on nd strip-to-strip calibration work

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