Update the sTGC strip cluster profile
Recent studies of sTGC cluster charge find that the strip cluster profile can be described by a double Gaussian function. The parameters of the double-Gaussian curve remains relatively constant for incident angles between 10 degrees and 30 degrees (and over the full geometric coverage of the sTGC detector). The best-fitted double-Gaussian curve for an incident angle of 30 deg is shown below.
Therefore, this merge request updates the charge model to use a double-Gaussian curve to describe the strip cluster charge profile (previously, a single Gaussian function was used). The parameters of the double-Gaussian curve are the best-fitted values at an incident angle of 10 degrees. With this update, the average strip cluster size is approximately 5.3, and is constant over the full range of incident angle as shown below (on the left).
The distribution in data is shown on the right. In these figures, angle theta is the angle of the track with respect to the beam line. Positive theta values indicate side A and negative theta values indicate side C.
The figures show the average cluster size in data is smaller than in simulation and is rising with the incident angle. The overall scaling is incorrect, since some tuning was done with the previous single-Gaussian cluster profile. The gas gain, VMM gain and channel charge threshold are the parameters that define the overall scaling. However, in this merge request, an additional global scale factor is added to scale down the average cluster size.
To describe the increase of average cluster size with angle, the total charge is multiplied by a factor \sqrt{1 + \alpha^2\ \tan^2(\theta)}, where \alpha is the parameter to be tuned with data. From an angle of 10 degrees to 30 degrees, the average cluster size increases from approximately 4.5 to 5.3. Therefore, \alpha is set to 4.0 in this merge request. Accurate estimate is not available at the moment, since a difference in the cluster size between the large and small sectors is under study. Once the difference is well understood, the value of \alpha should be reviewed.
The figure below shows the average strip cluster size with the changes in this merge request:
The spatial resolution remains unchanged (as it should be), since the peak of the cluster charge profile curve is not modified.
