Optimalisation of track reconstruction using vertex detector in the NA61/SHINE experiment

The main result of this thesis shows the first direct measurement of open charm hadrons ($\text{D}^0$ and $\overline{\text{D}^0}$) in the collisions of nuclei at the top energy of Super Proton Synchrotron (SPS). It was obtained from the data collected by the NA61/SHINE experiment and is the final result of the feasibility studies of new NA61/SHINE physics programme. The programme of charm measurements was motivated by the following questions: - What is the mechanism of open charm production? - How does the onset of deconfinement impact open charm production? - How does the formation of quark-gluon plasma impact $J/\psi$ production? To answer these questions, one need to know the mean number of charm quark pairs $\langle c\bar{c}\rangle$ produced in a full phase space in heavy-ion collisions. Up to now, such a data does not exist and NA61/SHINE started the corresponding measurements in December 2016. Because of very short lifetime of open charm hadrons, a micro vertex detector is needed to perform the measurement. In December 2016, the Small-Acceptance Vertex Detector (SAVD) was installed and the first data for Pb+Pb collisions at 150\textit{A} GeV/\textit{c} were collected. The Vertex Detector will be upgraded during the Long Shutdown 2 at CERN (2019-2020). The first step of the data analysis was reconstruction. Two algorithms implemented as a part of this thesis were used: the algorithm of silicon sensors alignment and the algorithm of VD-TPC track matching. The geometry corrections were calculated in a way to minimise the distances between clusters and fitted tracks. The data collected without magnetic field were used, because then clusters created by one particle should lie on the straight line. The final corrections improved the spatial clusters resolution up to 20\%. The track matching was done using the method via interpolation. At first the tracks were refitted to primary vertex reconstructed by Vertex Detector (for primary tracks) or to VD cluster from second station (for secondary tracks) and then interpolated to VD stations in order to collect the matching clusters. The implemented algorithms were tested on the analysis of K$^0_\text{s}$ signal. The signal was successfully observed but the analysis showed the calibration problem of a part of the collected collisions. Thus, for the final analysis only properly calibrated data were used. As the most important result, the invariant mass distribution of reconstructed secondary tracks was obtained, assuming the pion and kaon masses. It shows the indication of $\text{D}^0$ and $\overline{\text{D}^0}$ signal reconstructed from the decay channel: $\text{D}^0 \rightarrow \pi^+ + K^- $. This result allowed to validate the measurement concept and confirmed that NA61/SHINE is able to measure open charm hadrons.