New Algorithm of Seed Finding for Track Reconstruction

Event reconstruction is a fundamental problem in the high energy physics experiments. It consists of track finding and track fitting procedures in the experiment tracking detectors. This requires a tremendous search of detector responses belonging to each track aimed at obtaining so-called “seeds”, i.e. initial approximations of track parameters of charged particles. In the paper we propose a new algorithm of the seedfinding procedure for the BM@N experiment.


Introduction
BM@N (Baryonic Matter at Nuclotron) is a fixed target experiment at the JINR Nuclotron for the study of A + A collisions by measuring a variety of observables [1].The proposed set-up for this experiment is shown in figure 1.It combines high precision track measurements with time-of-flight information for particle identification and total energy measurements for event characterization.The charged particles will be a e-mail: dmitriybaranof@gmail.com b e-mail: Sergey.Merts@gmail.comc e-mail: gososkov@gmail.comd e-mail: rogachevsky@jinr.rumeasured with the set of GEM (Gaseous Electron Multipliers) detectors located downstream of the target inside the analyzing magnet of 0.8 T and drift chambers situated outside the magnetic field.Design parameters of the time-of-flight detectors based on multigap Resistive Plate Chambers (mRPC) with a strip read-out allow efficient discrimination between particle species with momentum up to a few GeV/c.The Zero degree calorimeter (ZDC) is designed for the collision centrality analysis by measuring the energy of forward going particles.The Recoil detector, partially covering the backward hemisphere (−1.0 < η < 1.2) near the target, is planned for the independent analysis of the collision centrality by the measurement of the energy of the target fragments.
The event reconstruction for the BM@N experiment consists in finding track seeds in the GEM detectors and then extrapolate them with the Kalman filter [2] to other detectors.As one can see from the left image of the figure 3, the seed finding problem is really hard and time consuming on any projection due to overcrowding the area of search by hits1 .To find a seed from the set of hits registered by a tracking detector one should classify somehow those hits by their closeness to particle trajectories.There are several methods used to achieve that, as Hough transform, elastic tracking, cellular automaton etc, with their advantages and shortcomings [3,4].We propose a new transformation of the coordinate system which results in a transformed space, where hits corresponding to a same track are grouped more compactly.

Track parameters and coordinate transformation
Let us consider a parametric helix equation that describes a charged particle trajectory in a homogeneous magnetic field (the direction of the magnetic field is parallel to the y axis): where r is the radius of the helix and c is a constant giving the vertical separation of the helix loops.
Let us make a substitution where Using (1) and (2) one can obtain the expressions: Getting t from the second equation of ( 3) and replacing it in the first equation of ( 3) we obtain a relationship between ỹ and x: The parameter k = r/c is directly related to the polar angle and the momentum of the track.For tracks to be reconstructed in the BM@N experiment the polar angle is less than 30 • and the momentum more than 100 MeV/c.The emerging k value is k > 100 and the helix (1) is transformed to the fast oscillating curve with almost horizontal waves, as shown in the figure 2.
Tracks in the BM@N experiment take only part of the helix and their transformation follows to central, approximately horizontal, fragments of the waves shown in figure 2. This can be observed in the figure 3 where simulated hits for Au-Au collision with E lab = 4 AGeV and their images after coordinate transformation {x, y} −→ {x/R, y/R} are presented.Algorithm efficiency evaluated by comparison of hit identifiers obtained by the algorithm with known Monte Carlo identifiers.The algorithm is a two-steps one: at the first step it is determined whether two strips crossing is a hit.Only if it is true then the second step is accomplished when all fakes are searched lying on the corresponding strips.Therefore the efficiency directly depends on the number of the found hits (see figure 5).

Using of potential approach for data contaminated by fakes
The fake contamination of data for the BM@N GEM detector brought us serious obstacles for carrying out our algorithm for track candidate search, as it is seen on the left panel of figure 6, where an UrQMD Au-Au event for the only last 5 stations even after {x/R, y/R} transform and fake rejection is presented.Applying and then summarizing this potential to every hit on this plane with properly chosen σ x and σ y , we obtain potentials of close hits form a peak, the amplitude of which depends on the corresponding particle momentum.On the right panel of the figure 6 the result of applying the Lorenz potential with σ x = 0.028, σ y = 0.00075 and amplitude cut equal 1.5 demonstrates the significant improvement of transformed data to which now the algorithm for track candidate search is applicable.
Although a direct potential application is time consuming, their compactness allows to reduce the computational procedure to a faster sliding window liable to be parallelized.

Conclusion
A new algorithm of searching for track-candidates has been proposed and tested for BM@N data.The developed algorithm allows considerable decrease of combinatorics.A high speed of execution of the algorithm has been achieved.A new approach applying Lorenz potential to improve track-candidate search in cases of high multiplicity is proposed.The study of fake hits appearance was fulfilled and effective procedures for the fake rejection were proposed.

Figure 1 .
Figure 1.Set-up of the BM@N experiment DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 201

Figure 6 . 2 x+ 2 y
Figure 6.UrQMD Au-Au events in {x/R, y/R} space for last 5 GEM-stations.Left: before Lorenz potential applying.Right: after applying the potential