Reconstructing charged-particle trajectories in the PANDA Straw Tube Tracker using the LOcal Track Finder (LOTF) algorithm

Abstract

We present the LOcal Track Finder (lotf) algorithm, a method that performs charged-particle trajectory reconstruction using the Straw Tube Tracker, one of the central trackers of the antiProton ANnihilation at DArmstadt (PANDA) detector. The algorithm builds upon the neighboring relations of the tubes to connect individual hits and form track candidates. In addition, it uses a local fitting procedure to handle regions where several tracks overlap and utilizes a system of virtual nodes to reconstruct the z-information of the particle trajectories. We generated 30,000 events to assess the performance of our approach and compared its global track assignment efficiency with respect to two other track reconstruction methods. lotf has (1) an average of 85% of found tracks, (2) the largest number of Fully Pure tracks, (3) the lowest amount of incorrect reconstructions, and (4) is significantly faster than the other two approaches. Further, we compared the z-reconstruction performance with one of the two alternative methods and show that lotf improves the median z-error by a factor of 8.7. Finally, we tested our method using 3750 data sets composed of 4 events each, demonstrating that our approach handles cases in which events are mixed. The raw (without parallelization) average reconstruction rate is about 68,000 hits/s, which makes the present algorithm promising for online data selection and processing.

A Algorithms

In this section, we present the code of the algorithms used in the present work.

1.1 A.1 The connect phase

In Sect. 3.1.1, we briefly presented the connect phase. In this appendix, we present and detail the corresponding pseudocode in Algorithm 1. The function FindStartingHits looks for the edges of the track by extracting all nodes that belong to the inner- or outermost layer of the STT (the “limit layers”). Every time we find such a node, we define a new track candidate using the structure PathCandidate and set the current node as the tail of the track. Neighbors of this node are extracted and stored in the neighbors vector. We use a variable CurDir to determine the current orientation of the track, based on the layer of the nodes that have been added so far (layer 0 being the closest to the beam-target interaction point). The CurDir variable is either UP, DOWN, or SAME depending on whether the layer index difference of the two most recently added nodes is 1, $-1$, or 0, respectively.

We connect neighboring activated tubes iteratively to a track using a loop that successively looks for the next available neighbors around the most recently added node. If we have a single activated tube, it is automatically connected to the track. Otherwise, we use the procedure SortPerLayer to sort all the available neighboring nodes based on their layer index. We then add only neighbors that are consistent with the track direction and are adjacent to each other (function AreConnected). If the layer configuration of all neighbors is too complex (i.e. we have neighbors on all different layers and the track direction is unclear), we pause the track reconstruction and store the current list of neighbors. Then, the track reconstruction is resumed during the fitting phase to resolve these complex cases.

The track reconstruction also stops when we have no more neighboring nodes in sight. For the latter case, we test whether the current track looks complete by testing if its tail node (the first node added) and head node (the last node added) are on layer limits. This criterion assumes that a track transiting through the entire STT volume or circling in it is finished. If a track has no more neighboring nodes but one of its extremities ends in the middle of the STT, we flag it as ongoing for later investigation. Indeed, there might exist another track candidate, not directly neighboring, that it can be connected to.

1.2 A.2 The fitting phase

Algorithm 2 details the steps described in Sect. 3.1.2. For all the tracks flagged as ongoing, we use a local fitting approach based on a system of anchor nodes to look for the next best node to add to the track. The function ExtractLast3Anc recovers the last three anchors in the track that are used to fit the parametric equation system for the x and y coordinates (function FitXYLine). The variables xPred and yPred are the predicted coordinates of the next nodes according to the parametric equations. For all the neighboring nodes, we compute the distance (labeled hitDist) between the node position and the predicted coordinates of the next hit using the function ComputeDist. Additionally, we use the anchors to determine the track direction (CurDir) which is derived based on the layers the anchors belong to (similar to the method used during the connect phase). Once we tested all the hits, we look for the best possible fit in the list by taking the node with the minimal distance while having a consistent direction with respect to the CurDir variable. This is done using the function FindBestHit. As detailed in Sect. 3.1.2, we set a criterion on the maximum distance acceptable such that the function returns $-1$ if no neighboring nodes are sufficiently close to the predicted node position.

When a good node is found, if it already belongs to another track, we check whether these tracks should be merged using the function CheckMerging which computes the intersection angle between two tracks. If the CheckMerging test is successful (see Sect. 3.1.2), the fitting phase for this particular track is stopped, and both tracks are flagged as ToMerge such that no more hits are added.

On the other hand, if CheckMerging returns false, or if the best node found does not belong to any track, we connect this node to the current track. We repeat the steps above updating the list of neighbors to include the neighbors of the most recently added tube. The algorithm continues until the current track is flagged for merging, or until the list of next neighbors is empty.

1.3 A.3 z-reconstruction

In this section, we detail the pseudo-code for the procedures used for the z-reconstruction in Algorithm 3. The CorrectSkewedXY procedure is the function used to estimate the exact hit position along the tube (see Fig. 10). The procedure InterpolateZCoord is the function used at the end of the track reconstruction to fit a parametric line in the z-direction and re-estimate consistently the z coordinates of all the nodes in the track. The functioning of the two procedures is detailed in Sect. 3.2.