Asymmetries in mixed beauty decays

The understanding of fundamental processes in nature has greatly improved over the last century. This has lead to the ambition to explain large-scale cosmological observations starting from the very small scale of particle interactions. In doing so, the Standard Model (SM) of particle physics is unable to explain the large matter-over-antimatter dominance that we observe in our universe. Physics beyond the SM, in the form of additional particles and forces, may help to explain this difference. In this thesis, the search for new physics is done by precisely measuring processes that are sensitive to the contribution of unknown particles through quantum loops. If a deviation from the SM prediction is observed, new physics can explain the difference. In this thesis, the sensitive process that is measured is $C\!P$ violation in the mixing of $B_d$ and $B_s$ mesons, called $a_{\text{sl}}^{d}$ and $a_{\text{sl}}^{s}$ Recent measurements by the D0 collaboration have hinted that these rates might be different at three standard deviations. Exploiting the high energy and luminosity of the $pp$ collisions at the Large Hadron Collider (LHC), the LHCb detector has collected data about millions of $B_d$ and $B_s$ meson decays. While this detector is specifically designed to perform such measurements, the level of precision allowed by this amount of data requires careful inspection of all possible sources of asymmetries in the detection; a higher detection efficiency for matter with respect to antimatter would artificially induce a non-zero measurement of the $C\!P$ asymmetry. After careful calibration of these detection asymmetries using data-driven techniques, the obtained values are \begin{align*} a_{\text{sl}}^{d} &= (-0.02 \pm 0.19 \pm 0.30 )\% , \\ a_{\text{sl}}^{s} &= (0.39 \pm 0.26 \pm 0.20) \% , \end{align*} which are the most precise measurements to-date. They agree with the SM predictions, and are only marginally compatible with the D0 anomaly. The role of these analyses in future searches for new physics is complementary to that of other measurements of $C\!P$ violation, with ample room for a 5-standard-deviation discovery after the upgrade of the \lhcb detector.