Precise measurements of the $W$ boson’s mass and lepton flavour universality, and trigger development with the LHCb experiment at CERN

In the electroweak sector of the Standard Model (SM), comparing precise measurements with predictions built on the SM's assumptions offers one of the principal avenues for indirect discoveries of new physics. The $W$ boson mass, $m_W$, is a key SM parameter that is notoriously difficult to measure at hadron colliders, and the lack of high-precision measurements of it limits the sector's discovery power. Meanwhile, the SM's fundamental property of lepton flavour universality (LFU) has been questioned by hints of discrepancy in recent measurements of rare $B$-meson decays and legacy tests of $W$-boson decays. This thesis presents two measurements using LHCb's 2016 data that address these important issues: first, a proof-of-principle extraction of $m_W$ that paves the way for a competitive legacy measurement; and second, a test of the $W$ boson's LFU in decays to tau leptons and muons that, when completed, will validate and complement other recent measurements shedding light on previous LFU anomalies. The value of $m_W$ was measured to be \begin{equation*} m_{W} = 80354 \pm 23_{\rm stat} \pm 10_{\rm exp} \pm 17_{\rm theory} \pm 9_{\rm PDF}~\rm{MeV} \, , \end{equation*} which is consistent with previous direct measurements and indirect SM predictions. It is not consistent with the very-recent CDF measurement, and therefore places LHCb in prime position to address this high-profile disagreement with a future measurement using all available data. LHCb is currently undergoing commissioning for a fresh period of data-taking, which features a brand-new detector, a factor of five more collisions and a fully redesigned trigger system. The development of the trigger validation tool $\texttt{HltEfficiencyChecker}$ is also presented, which plays a crucial role in facilitating trigger optimization that fully exploits the new detector, whilst also conforming to its constraints. This tool helped the collaboration decide that the new first-level trigger should be implemented with GPUs, and is now widely used in LHCb, as exemplified in the development of trigger selections for electroweak processes in Run 3 presented here.