A Study of the CMSSW Rechit Versus Trkfnd Tracking Resolution

A Study of the CMSSW RecHit versus TrkFnd Tracking Resolution

L. S. Durkin, Ohio State U. and N. Ippolito, Purdue U.

May 23, 2006

We have recently completed a CMSSW module to compare full output from the

TrkFnd1-3 track finding and fitting program with the present output from CMSSW RecHit program. The data analyzed in this report comes from cosmic ray RUN00000027. The comparisons were done with cosmic ray tracks in ME/2/2/27. Only events with a single three-dimensional track and greater than or equal to five cathode hits on the track were used.

TrkFnd in performing pulse width (Gatti Distribution) fitting uses a full 3-time bin by 3-charge bin fit to clustered strip ADC distributions. Full gain, cross talk, and correlated noise coefficients are employed to fit this distribution to determine the track position. The cross talk correction employs detailed shapes4-7 of the cross talk as a function of time.

In contrast CMSSW RecHit was written to analyze ORCA Monte Carlo output. This is one of the first times RecHit positions have been determined using actual data. RecHit Gatti fitting uses a 1-time bin by 3-charge bin fit to clustered strip ADC data. No constants or noise coefficients are employed in the fit with the exception of a single cross talk coefficient.

CMS RecHit also assumes all cathode amplifier pulses peak in time bin 4. Although true in the Monte Carlo this is definitely not true in real data. Electron drift time to the anode wires is around 80 nsec with a wide variation. Shown in Figure 1 below is the peak time bin for real data in ME2/2/27. The timing has been set so roughly half of the data peaks in time bin 4 and half in time bin 5.

Figure 1 – Peak Time Bin (8 time samples beginning at 0)

To test the effect of this erroneous choice in Figure 2 & 3 the difference between the full TrkFnd reconstructed position and the full RecHit reconstructed position is histogrammed separately in time bin 4 and time bin 5. Clearly one needs to analyze the charge data near the peak of the distribution to get even slightly reasonable resolution. Even in Figure 2 the position differences are large. Both program after all are analyzing the same ADC data for the Gatti fitting. It is hard to believe, but true, there are differences between the two programs as large as 0.5 strips.

Figure 2 – Reconstructed position difference between TrkFnd and

RecHit for hits with peaking time in time bin 4.

Figure 3 – Reconstructed position difference between TrkFnd and

RecHit for hits with peaking time in time bin 5.

Putting aside for the moment the peak time problem, we proceed plotting RecHit data from pulses which peak in time bin 4. This will give a clear indication of the present status of Gatti fitting in RecHit after this peak time problem is resolved. Shown in Figure 4 is the track residuals, fitted track minus the fully corrected hit position, for the TrkFnd program. As always the resolution is better between strips (Gatti position -0.5 and 0.5) than at the center of the strip (Gatti position 0.0).

Figure 4 – TrkFnd track residuals vs. position of

hit within the strip.

Figure 5 – RecHit track residuals vs. position of

hit within the strip.

In Figure 5 are shown the same track residuals for the RecHit algorithm. The fitted line from TrkFnd has been used to calculate the residuals. It is obvious and not surprising that the RecHit resolution is much worse. This can be attributed almost exclusively to the poor cross talk correction, although some is no doubt due to a 1x3 (time bin, charge bin) fit versus a 3x3 (time bin, charge bin) fit.

In closing some other pitfalls in the RecHit algorithm should be noted. In order to perform Gatti fitting one needs to know the anode position (Strip width depends on radial position). The RecHit algorithm does this by forming hits from all possible combinations of anode and cathode hits in the same plane. This has the disadvantages that is requires both an anode and cathode hit in each plane increasing hit inefficiency. Additionally there may be many anode cathode pairs thus slowing the algorithm with many unnecessary Minuit fits. In contrast TrkFnd finds and fits an anode track before doing Gatti fitting, solving both of the disadvantages in the RecHit algorithm.

References

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