Determination of the b-hadron production cross-section and measurement of CP violation in $B_s^0 \to \phi \phi$ decays at the LHCb experiment

The production cross-sections of beauty hadrons in proton-proton collisions at centre-of-mass energies of $\sqrt{s}$ = 7 TeV and $\sqrt{s}$ = 13 TeV are determined with semileptonic b-hadron decays in the first part of this thesis. Using the collected data samples that correspond to integrated uminosities of L = 284 pb$^{−1}$ and L = 4.60 pb$^{−1}$, the cross-sections in the LHCb acceptance, the range in pseudorapidity $\eta$ from 2 to 5, are determined to be 69.0 $\pm$ 0.3(stat) $\pm$ 6.1(syst) $\mu b$ and 137.5 $\pm$ 1.1(stat) $\pm$ 12.8(syst) $\mu b$ at $\sqrt{s}$ = 7 TeV and $\sqrt{s}$ = 13 TeV, respectively. A good agreement of the $\eta$-dependent cross-sections and their ratios is found between the data and theoretical fixed-order next-to-leading log (FONLL) calculations. The production rate of b hadrons allows for precision measurements of physics parameters in rare b-hadron decays that offer a great sensitivity to test the quantum corrections predicted by the Standard Model and to probe possible contributions from physics beyond the Standard Model. Time-dependent CP violation in $B_s^0 \to \phi \phi$ decays is a sensitive observable which could be influenced by new heavy degrees of freedom contributing to the loop-induced $B_s^0$ mixing and decay processes. The measurement of CP violation in this decay mode is performed in the second part of this thesis with the LHC Run I dataset corresponding to an integrated luminosity of 3 fb$^{-1}$. The CP-violating phase is determined to be $\phi_s (B_s^0 \to \phi \phi)$ = −0.17 $\pm$ 0.15 (stat) $\pm$ 0.03 (syst) rad which is compatible with Standard-Model predictions of zero. No evidence for physics beyond the Standard Model is found. Most of LHCb’s current measurements are limited by statistical uncertainties. To overcome this shortcoming, LHCb plans to upgrade the detector after 2018. Starting in 2021, the detector can be operated at a higher instantaneous luminosity with a triggerless 40 MHz readout system. Amongst others, the current main tracking detector will be replaced by a scintillating fibre detector. The third part of this thesis presents the measurement of the performance of prototype modules of this tracking detector. The spatial resolution is determined to be 77.2 $\pm$ 1.3 $\mu m$ and the single-hit detection efficiency is measured as 98.8 $\pm$ 0.1%, which meets the requirements of the new tracking detector.