The reconstruction of charged particle trajectories in the CMS endcap muon system is based on hits detected by the Cathode Strip Chambers. The reconstruction procedure for these multilayer detectors can be divided into two main parts: the reconstruction of hits on each layer, and the assembly of track segments within the chambers from the reconstructed hits. At the HL-LHC the increased luminosity implies higher muon and background rates which, without improvement of the existing hit reconstruction algorithm, may deteriorate the present performance of the Cathode Strip Chambers system. On one hand, the increasing hit rates will require a better precision in the identification of two or more particles that pass very close to each other. On the other, upgraded readout electronics for the Cathode Strip Chambers provides options for improved reconstruction, which have not yet been fully exploited in offline software. Some proposed solutions for these issues, together with figures comparing the standard and improved reconstruction algorithms, are presented here.
The Cathode Strip Chambers (CSCs) are the main detectors of the endcap muon system of the
CMS experiment [
The signal from wires, along with the charge distribution from strips, gives us a 2D coordinate of the passing particle on the layer. If we have such coordinates on at least 3 layers, it is possible to assemble them into segments and reconstruct the entire trajectory of the charged particle in the particular chamber. Information from several CSCs, along with information from other detectors, is gathered together in order to reconstruct the entire trajectory of the passing particle, starting from the interaction point and up to the limits where it exits the frame of the CMS detector.
While developing a new segment building algorithm for CSCs [2], it was noticed that in some
cases the segment builder struggled to add hits on the segment due to the fact that they have a poor
reconstruction accuracy in terms of the strip coordinate. The strip coordinate is estimated by fitting the
strip charge distribution with the Gatti function [
The development of a new wavelet-based reconstruction algorithm for the strip coordinate was initiated in order to improve the strip coordinate reconstruction for overlapping signals. The g2-WTS (Wavelet-TranSform method based on the use of second degree wavelets ( 2)) [4] was chosen by us for overlapping signals recognition.
The main function in the wavelet analysis is the following double Gaussian function 2 2
G(x; A, x1, 1; B, x2, 2 ) = Aexp(− (x2− x121) ) + Bexp(− (x2− x222) ) (1) We build 2, 3 or 4 Gaussians on the chosen interval of strips with a constant step as a first approximation. For the case of three overlapping signals the formula (1) looks as follows: ( ; 1, 1, 1; 2, 2, 2; 3, 3, 3) = 1 −( 2− 121)2 + 2 −( 2− 222)2 + 3 −( 2− 323)2
The parameters 1, 1, 2, 2, 3, 3, 1, 2, 3 of the overlapping signals are obtained by fitting the data distribution to the sum of these three Gaussians in each coordinate x. (2)
An example of two overlapping signals recognition is shown in Figure 2. The green line that corresponds to the simulated muon coordinate coincides exactly with one of the signals recognized by the proposed algorithm (red lines), while the standard approach (blue line) misses by almost half of a strip width.
Overall the new approach shows better results than the standard approach (fig. 3). But the time consumption in the framework of the CMS software is still unknown because at the moment it is a standalone tool adjustable for any input data. This may be crucial, because the wavelet approach is an iterative method and there are strict limits for the time spent for the reconstruction of the CMS event, especially within the trigger.
A much simpler approach for two overlapping signals recognition was also developed. The shape of the strip charge distribution coming from two overlapping signals can be easily detected. It usually comprises 5 or 6 strips that have charges above the pedestal level. They contain one maximum, and the shape of the distribution is not regular. We treat such cases as two signals overlapping, where one maximum is clearly noticeable and the second one is hidden at one strip distance from the main maxima. If such a distribution is found, it is divided into two simple and regular distributions by sharing the charge from the common strip between two maxima proportionally to their charges (fig. 4).
As a result the overall number of reconstructed segments increases, and their ^2 ⁄ becomes smaller (fig. 5). It means that the application of the proposed approach gives us the opportunity to reconstruct more segments and their overall quality improves.
Aspects of the detector geometry have led to inefficiencies in specific regions of the CSC
muon detectors. The ME11 chambers are the closest CSC chambers to the interaction point. In order
to be able to reconstruct trajectories of passing particles at high rates, a special geometric design was
implemented in these chambers [
The application of the wavelet analysis gives us the possibility of reconstructing the strip coordinate ~2.5 times closer to the simulated muon in comparison with the standard approach, although the iterative method most likely will be too time-consuming. A simpler way to divide overlapping signals is also proposed. It is limited to two overlapping signals delimitation and the comparison in performance with the wavelet approach is ongoing.
The hardware upgrade in particular chambers made it possible to improve hit reconstruction. The regions that were suffering from the lack of reconstructed hits can now be fully used for hit and segment reconstruction.
There are multiple places for improvements in terms of hit and segment reconstruction in CSCs. Different approaches can be used for solving the same problem. The main objective is to get as much and as accurate information as possible for further steps of particle trajectory reconstruction.