Cathode Strip Resolution

Preliminary Fitting Data from Test Beam 2003

S. Durkin

Ohio State University

Introduction

I have been able to reproduce the resolution for CSC cathode strips obtained in previous CMS CSC test beams. This is remarkable in that no gain or cross talk constants were used in the analysis. Further there were known gas problems in the CSC for the runs I have analyzed. Below I describe the procedure used. The code though preliminary is available from trackfitting.tar. It is compatable with the C++ code although written in C.

Track Finding

The beam was clean enough that no detailed track finding was necessary. I chose the largest charge deposition in each plane as my track points. In the very rare case there were extra hits around I threw out the event. The code used cat be found at this link. Anode positions necessary for fitting were found in an equally naïve fashion.

Notation

The charge in a strip will be denote as where X=L,M,R (left, middle, right) and T (nanoseconds) corresponds to the time bin with respect to the maximum charge time bin. Nine bins will be used in this analysis:

The largest charge deposition corresponds to .

Pedestal Subtraction

The standard method of subtracting off the first two time samples was employed.

Precision Sampling Time

Cross talk is a strong function of the exact time of peak charge, ts, within the time bin with the largest charge deposit. To find this the three charge deposits were fit to a 5-pole semi-gaussian expected from the buckeye shaping:

The peaking time was fixed to 133 nanoseconds. The fit was a simple chi-squared minimization. The code can be found on this link.

Cross Talk Determination

To determine the cross talk the data was broken into bins in ts. A chi-square fit of the L,M,R charge depositions as a function of distance from a fit track (a smeared gatti distribution) was then performed. The code for the smeared gatti distribution can be found on this link.

In the first plot is plotted versus ts for track hits that passed within 1mm of the center of the strip. The red corresponds to T= -50 nsec, the black to the largest deposit T=0 nsec, and the blue to T=50 nsec. A clear correlation is observed. There is large cross talk in the red region and nearly no cross talk at all in the blue region. This is consistent with the capacitative+slightly resistive coupling between adjacent strips.

In the second plot is shown fits to the smeared gatti distribution as a function of ts. The black gatti curve corresponds to the earliest ts bin while the red gatti curve corresponds to the latest ts bin. The fit lines are drawn through the curves.

The last plot displays the cross talk vs ts curve obtained from the fitting. Since the cross talk is capacitive it can be negative. The C-routine to obtain this correction is available at this link.

Position Coordinate within a Strip

Once the cross talk is known, one only needs to know the gatti h parameter to perform this fit. For ME2,3/2 the h parameter should be h=0.475. For some unknown reason h=0.490 seem to fit the distributions better. Since the strip with varies as a function of radius along the strip this must be accounted for. It is most convenient to work in coordinates of strip with rather than meters. The h parameter input into the gatti function to convert to strip widths is:

where xa is the anode wire group the track passed through.

I have performed a chi-square fit to the 9 charges as a function of three normalization constants (one for each sample), and the hit position y leaving 5 degrees of freedom.

The code for this link can be found at link. A uniform error has been used for each charge which is a simplification. This was determined to produce a properly normalized chi-square distribution for 5 degrees of freedom (see plot) with no dependence of the size of the charge deposit. A final noise of 2.7 counts with a systematic error of 0.008*(total charge) worked well. Measured noise on adjacent strips was measured to be 3.2 counts. I attribute this difference to the fact the noise is actually correlated.

Cathode Noise Correlation

The peak charge distributions for the test beam tracks were located in time bins 4 and 5 (counting from 0). I have measure the noise correlation coefficients for time bins 3,4,5, and 6. As before this data was pedestal subtracted using bins 0 and 1. The data is shown below(in counts) and histograms of the covariances can be found here:

	Q3	Q4	Q5	Q6
Q3	16.35	-	-	-
Q4	8.81	13.96	-	-
Q5	4.85	6.93	12.36
Q6	4.57	4.21	6.34	12.18

It is seen that the correlation coefficients are rather large. These should probably be taken into account in future fitting of the charge distributions.

I have also measured the noise correlation coefficients between adjacent bins shown in the table below and histograms of the covariances can be found here:

	Q3	Q4	Q5	Q6
Q’3	1.07	.56	.69	.51
Q’4	.19	.14	-.28	.92
Q’5	.70	-.19	-.39	-.33
Q’6	.46	.84	-.44	-.33

These are probably small enough to be ignored in future fitting.

Track Fitting

The final coordinates were then calculated for each layer as:

x = layer #

y = strip # + offset + y(gatti from above)

The offset position for the planes was fit and found to be(in strip units):

-0.002,-0.493,-0.005,-0.496,-0.001,-0.499

Thus the layers are fit to have less than ~70 micrometers displacement.

A least squares fit was performed on these coordinates. The errors output by the gatti coordinate procedure (above) were used in the fit. Unfortunately these errors did not yield a proper chi-square distribution. It was necessary to arbitrarily multiply each of the errors by 1.5 in order to get reasonable chi-squares. This discrepancy is not presently understood. Removing the coordinate being measured in the fit minus slope and angle yields 3,2, and 1 degree fits for 6,5, and 4 planes hit respectively. Show in the following three plots are the chi-squares versus theory using these kludged errors.

Click on the following link to get 50 fit tracks (event_plts.pdf). In these plots a red circle indicates the point was used in the least squares fit.

Results

The results are for RUN000260 and the first chamber. As was mentioned previously the gas used for this first set of runs was the wrong mixture. The plateau curve was substantially higher, and as a result the pulse heights in the chambers were rather low. The typical strip had a landau peak of ~100 counts.

To find the resolution a track was fit excluding the plane being used. Using the least squares fit results one can calculate the expected resolution of the track at each plane. If this is small then the residual is just the hit minus the track position. Unfortunately this is large except for the central two planes. Show in these two plots is the fit track resolution expected at each plane. The first histogram show the track uncertainty at a function of plane. Red corresponds to planes 0 and 5, blue to planes 1 and 4, and black to planes 2 and 3. Clearly only in the middle two planes is the accuracy good enough to extract meaningful plane residuals. The second histogram is the same histogram averaged over planes for 5 plane tracks (black), 4 plane tracks(red), and 3 plane tracks (blue). Once again it is seen that one needs all planes in the fit.

Thus looking at only planes 2 and 3 I extracted the chamber resolution. The results are similar to previous test beam results. Show in the following plots are the results. Plot one shows a scatter plot of residual versus position in the chamber. At the center of the strip the position resolution is poor, and it gets much better toward the edge of the strips. Binning this resolution in position and determining the resolution in each bin yields the second plot. Here the track uncertainty has been removed in quadrature.

Lastly the resulting position resolutions are well predicted by the kludged errors from the gatti fitting position. Show in the following plot is these errors versus position in the strip. Qualitatively these agree well with the previous plot.

We will run in a week or so with better gas in the chambers. This analysis will be redone at that time.

Update (June 18, 2003)

The previous results were verified with a new run taken with the proper gas. The results were nearly identical (slightly better resolution near the wire). The analysis is still limited by track position errors. I have done a global fit to the two chambers. This seems promising since the track position errors disappear. I am still tuning parameters.

I have implemented a version of gatti-fitting (see code) with the full matrix fit included. This indeed changed the chi-square kludge of 1.5 meantioned above, but qualitatively changed little else. A new plot of the gatti-fit chi-square can be found here. The new chi-squares for the track fits with no kludge factor can be found here.