Update on My 'Toy' ND s2s Calibration

Introduction

As an exercise in understanding the complexities of the ND sts calibration I have been writing some code to generate my own calibration constants and have been comparing these values with those in MC. So far I have encorporated:

• Basic pre-selection of events and muon track hits
• Truncation of SigLin histograms for each strip to remove Landau tail effects
• Attenuation correction
• Basic path length through scintillator correction

I shall describe the methodology I am employing for each of these steps and show some results.

Methodology

My event pre-selection is as follows:

• number of tracks in event = 1
• track is at least 40 planes long
• at least 10 of these planes are classified 'track-like'
• difference in track vertex between U and V views <= 10 planes
• difference in track end between U and V views <= 6 planes
• path length through scintillator < 1.3 cm
• if:
  • shower energy = 0 - include all track hits
  • 0 < shower energy <= 10 - remove 1st 20 planes
  • 10 < shower energy <= 20 - remove 1st 30 planes
  • shower energy > 20 - remove event

I have yet to encorporate any cuts on the hits themselves and will include in the near future:

• checks that each hit is inside the detector

I then fill histograms for each strip with the SigLin values for any muon track hits that occur on that strip. I also make histograms that have these SigLin distributions truncated at 80% of the maximum value.

I take the means of the regular and truncated histograms and use them to construct 2 sets of calibration constants. Firstly the values are corrected for attenuation using the Calibrator GetAttenCorrectedTpos() function that takes as arguements; the strip end ID, the hit 'lpos' and the SigLin value. The lpos value is obtained by using the 'trk.stpu' value if the hit occurs in a V plane and the 'trk.stpv' value if the hit occurs in a U plane.

These attenuation corrected values are then scaled by a path length correction that I calculate in the following way:

• For the first hit on the track I calculate the angle subtended by a line joining the first and second hits with the z-axis.
• For the second to penultimate hits I calculate the angle subtended by a line joining the hits directly before and after the one in which I am interested with the z axis.
• For the last hit I use the line from the penultimate hit to the last hit to calculate the angle.
• In each case the cosine of the angle, theta_z, can be thought of as 'strip thickness(=1cm)'/real distance through scintillator. Then the real path length through scintillator is 1/cos(theta_z) and the correction factor is 1/(1/cos(theta_z)) = cos(theta_z). This correction factor is then always <= 1 as it should be to correct the SigLin values down.

I then use the mean of these corrected means to define the value to which all strips will be calibrated.

Results

The following figure shows the effect of the event pre-selection on the SigLin means distribution for:

• All ND U planes - top left
• All ND V planes - top right
• Calorimeter U planes - bottom left
• Calorimeter V planes - bottom right

where the calorimeter is defined as planes up to and including 120, the black histograms are the SigLin mean distributions before any event pre-selection and the red histograms after:

Figure 1.

It can be seen that the basic event pre-selection is having very little effect. This is because all the hits used, even before selection, lay on the longest track in an event and these tracks often pass all the selection criteria.

The attenuation correction comes from mapper data via the Calibrator. I am correcting for the attenuation before I correct for the muon path length through scintillator - I think this is the right way around as it is the non-path length corrected signal that gets attenuated along the fibre in reality. The following plot shows the SigLin response for all the hits in my sample as a function of distance from the strip centre and then the corrected SigLin values as a function of distance from the strip centre:

Figure 2.

This is just a pictorial representation of the correction as it exists in the MC.

The following plot shows a histogram of the path lengths through the scintillator for all of the hits in my sample:

Figure 3.

This looks as I would expect considering that I am using beam MC where most of the muons will be travelling close to parallel with the z axis. The following plot shows the SigLin response as a function of path length for all of my hits and then the path length corrected values:

Figure 4.

It is hard to see whether my basic path length correction is doing anything but the plot does show that either way the beam MC is such that the path length correction becomes less important than when using cosmics.

Having gone through these steps I then produce a set of calibration constants and compare these strip-by-strip with the MC values. The following plots show the errors on my produced constants for a given subset of the corrections for the whole ND and just for the calorimeter:

• Black - no cuts/corrections.
• Red - pre-selection cuts.
• Blue - pre-selection cuts and path length corrected.
• Pink - pre-selection cuts and attenuation corrected.
• Cyan - all cuts/corrections.

Figure 5.

The following tables give some of the statistics for the above plots:

I have not tabulated the results for the constants derived from the truncated mean distributions but they are very close to the values given here using the means. It can be seen that the only correction that is really doing any work here is the attenuation correction. I plan to refine my basic pre-selection and path length corrrections as they are fairly preliminary at the moment.

The means when I consider the whole ND are systematically different from 0.0 and this is because in the MC the 'average response per strip' value from which the constants are derived is made considering only the calorimeter planes with the spectrometer planes all having a constant of 1. This problem hence goes away somewhat when I only consider the calorimeter planes.

The following plane v.s. strip maps show where the problem strips are when all cuts have been applied:

Figure 6.

Conclusions and Further Work

I have a much better understanding of the strip-to-strip calibration and have had a go at incorporating some of the necessary corrections to a MC sample of events. My derived constants have then been checked against the MC values and the differences shown. I am planning next to:

• Improve event and hit pre-selection (rock muon-like sample?)
• Leave the path length correction for now as am working with beam MC
• Try to understand and then include the 0pe and 1pe corrections
• Try running over some data just to see what comes out