First observation of decay mode ${\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+}}$ and study $Z$ boson polarisation at the LHCb experiment

The Large Hadron Collider (LHC) is the most powerful and energetic particle accelerator in the world. The LHCb experiment is a signle-arm forward spectrometer situated at the LHC, which is primarily designed for the precision study of beauty and charm flavoured hadrons. In this thesis, the observation of a new decay mode for the doubly charmed baryon $\Xi_{cc}^{++}$ and the study of the angular coefficient of the $Z$ boson using the $pp$ collision data collected by the LHCb detector are presented. Besides physics analyses, I also made contributions to the SciFi detector upgrade and ghost probability algorithm for LHCb RunIII data taking. The Standard Model (SM) predicts the exist of the doubly charmed baryon $\Xi_{cc}^{++}$. It was firstly observed by the LHCb collaboration in 2017, using the decay model $\Xi_{cc}^{++}\to \Lambda_{c}^{+}(\to p^{+} K^{-} \pi^{+}) K^{-} \pi^{+}\pi^{+}$. Following the previous discovery of $\Xi_{cc}^{++}$, this thesis presents an observation of new decay model $\Xi_{cc}^{++}\to \Xi_{c}^{+}(\to p^{+} K^{-} \pi^{+})\pi^{+}$ for the first time, with a statistical significance of $5.9\sigma$, which confirmed the previous observation of the $\Xi_{cc}^{++}$. The data sample used in this observation is corresponds to an integrated luminosity of $1.7 \rm{fb}^{-1}$, collected by the LHCb experiment in $pp$ collisions of 2016 at a center-of-mass energy of 13TeV. The mass of the $\Xi_{cc}^{++}$ state was measured to be $3620.56 \pm 1.45 \ (\rm{stat}) \pm 0.49 \ (\rm{syst}) \ \rm {MeV}/c^{2}$, where the first and second uncertainties are statistical and systematic, respectively. The result is consistent with the previous result. The ratio of branching fractions between the decay model $ \Xi_{cc}^{++}\to \Xi_{c}^{+}(\to p^{+} K^{-} \pi^{+})\pi^{+}$ and $\Xi_{cc}^{++}\to \Lambda_{c}^{+}(\to p^{+} K^{-} \pi^{+}) K^{-} \pi^{+}\pi^{+}$. is measured to be $0.035 \pm 0.009 \ (\rm{stat}) \ \pm 0.003 \ (\rm{syst})$. Another physics topic presented in this thesis is a measurement of the angular coefficients of $\mu^{+}\mu^{-}$ pairs in the $Z$ boson mass region at LHCb. Measurements of the five most significant angular coefficients, $A_{0}$ through $A_{4}$, for $Z$ bosons produced in $pp$ collisions at $\sqrt{s}=13$TeV and decaying to $\mu^{+}\mu^{-}$ are presented as a function of the transverse momentum and rapidity of the $Z$ boson. The dataset used in this analysis is collected with the LHCb detector, corresponds to $5.2 \rm{fb}^{-1}$ of integrated luminosity. These measurements provide stringent tests on the SM, and comprehensive information about the $Z$ boson production mechanisms, and are compared to different theoretical predictions. The LHCb experiment is performing a major upgrade of the detector during the LHC Long Shutdown 2 from 2019 to 2021. This upgrade will enable the LHCb detector to operate at an increased instantaneous luminosity, and to record data at the LHC bunch crossing rate of 40 MHz. Besides the physics analyses, this thesis also includes two studies for this upgrade, for both the software and hardware upgrade. The new operating conditions require the replacement of the complete tracking system. The tracking stations downstream of the magnet will be replaced by the SciFi Tracker, which is a large and high granular scintillating fibre tracker. The performance of a full detector slice of the SciFi Tracker regarding the hit efficiency, hit resolution, and spillover has been studied using the data obtained during a test beam campaign at the CERN SPS in July 2018. For the software development in the LHCb, a neural-network based algorithm to identify fake tracks in the LHCb pattern recognition is presented. This algorithm, named ghost probability, is fast enough to fit into the CPU time budget of the software trigger farm and thus reduces the combinatorics of the decay reconstructions, as well as the number of tracks that need to be processed by the particle identification algorithms. For the upgrade, this algorithm is expected to be improved to deal with the highly increasing of online statistics in LHC Run-III, this thesis presents the latest updates on this algorithm.