## 2 Materials and Methods  
### Particle Competition of \(K_{s}\) and \(\Lambda\)  
The neutral particles \(K_{s}\)-mesons and \(\Lambda\)-hyperons serve as important indicators for the CBM experiment. \(K_{s}\) consists of a down-quark and a strange anti-quark, whereas \(\Lambda\) is build with an up-quark, down-quark and a strange quark. Theoretical predictions suggest that enhanced strangeness production (the production of strange, multi-strange or hyper-strange particles, that consist of one, two or three strange quarks or strange anti-quarks) is an indicator of deconfined matter [16], the Quark-Gluon Plasma. Both particles are abundantly created in the energy ranges of the experiment [15] and are therefore a reliable source of information. The two particles decay with the given probability BR (branching ratio) as follows:  
\[K_{s} \rightarrow\pi^{+}\pi^{-} (\text{BR}:69.20\pm 0.05\;\%),\] \[\Lambda \rightarrow\text{p}\pi^{-} (\text{BR}:63.9\pm 0.5\;\%),\]  
(please see [17; 18], respectively), and therefore both give a rise to negatively charged pions \(\pi^{-}\). Moreover, all daughter particles of \(K_{s}\) and \(\Lambda\) are non-neutral and, therefore, can be measured by the detectors and reconstructed by the algorithms. The particle reconstruction procedure combines all possible daughter particles, resulting in the simultaneous creation of a \"common\" pion, which is a decay product for both, the \(\Lambda\)-hyperon and \(K_{s}\)-meson, leading to the creation of these two possible mother particles, even though only one exist in the Monte Carlo simulated data. As a result, \(\Lambda\) and \(K_{s}\) create background noise for each other, which will hinder the physical analysis of the particles using real experiment data. Performing a particle competition to decide for the best-fitting mother particles helps to reduce this physical background noise by removing the falsely created mother particle candidate.  
The Kalman Filter (KF) Particle Finder [19] is an important package included in FLES, responsible for online reconstruction of short-lived particles and their decay chains. The package was updated recently by the Missing Mass method [20], and is now capable to reconstruct more than 150 different particle decays. Furthermore, it includes tools for performance measurements in the particle reconstruction process. The KF Particle Finder package reconstructs all possible mother particle candidates when a decay is recognized. Then, \(\chi^{2}\)-cuts and a particle competition are applied to select the best-fitting reconstructed particles and to reject the others. The existing implementation of particle competition has several stages. One of the most important steps is the evaluation of particle candidates' reconstructed mass values. Here, the algorithm examines the reconstructed particles' masses of each pair of candidates (competitors), and checks if one is within 3\(\sigma\) range of the known mass distribution peak, the so-called Particle Data Group (PDG) (which refers to a global collaboration of particle physicists, who define standards and publish results within the scope of research) mass. If one of them is within the range, the mass distance to the respective particle's PDG mass is used to determine the best-fitting mother particle.