Standalone track reconstruction on GPUs in the first stage of the upgraded LHCb trigger system & Preparations for measurements with strange hadrons in Run 3

The LHCb experiment is undergoing its first major detector upgrade to operate at a five times higher instantaneous luminosity during the Run 3 data taking period. It is equipped with a new set of tracking detectors (VELO, UT, SciFi) to match the conditions of an increased track multiplicity and radiation damage. The hardware trigger stage is removed. The first stage of the software trigger system is implemented to run on about 200 GPU cards with a throughput of 30 MHz. An alternative tracking algorithm called Seeding and Matching for the first trigger stage is developed and presented in this thesis. Other than the formerly used forward tracking, the presented algorithm performs the tracking without making use of the UT which allows to run in the early data taking of Run 3 before the UT will be installed. The Seeding is a standalone reconstruction of track segments in the SciFi, which is followed by a matching step where the SciFi seeds are matched to VELO track segments reconstructed beforehand. The physics and computing performance of the Seeding and Matching is evaluated and found to be compatible with the forward tracking. The Seeding and Matching is now used as the new baseline algorithm and currently being commissioned on the first Run 3 data. Furthermore, preparations for an early Run 3 measurement of the ratios of the production cross-section of $\Lambda^0$ and $K_\mathrm{S}^0$ hadrons are presented in this thesis.