Measurements of $CP$ violation in mixing of $B^0_s$ mesons and the $D^+_s$ production asymmetry at LHCb

This thesis reports two measurements performed using proton-proton collision data collected by the LHCb detector in 2011 and 2012, corresponding to an integrated luminosity of 3$\ \text{fb}^{-1}$ and centre-of-mass energies of 7 and 8 TeV respectively. The first measures the $C\!P$ asymmetry in $B^0_s$-$\kern 0.18em\overline{\kern -0.18em B}^0_s$ oscillations, called $a_{\rm sl}^s$. This is measured in inclusive $B^0_s$ and $\kern 0.18em\overline{\kern -0.18em B}^0_s$ to $D^{\mp}_s \mu^{\pm} \nu_{\mu} X$ decays, where the $D^{\mp}_s$ meson is reconstructed in the final state $K^{\mp}K^{\pm}\pi^{\mp}$. The measurement is performed in three regions in the Dalitz phase space of the $D^{\mp}_s$ decay, and corrected for detection and background asymmetries. A value of \begin{align*} a_{\rm sl}^s = (0.39 \pm 0.26\mathrm{\,(stat)} \pm 0.20\mathrm{\,(syst)}) \% \end{align*} is found, which is the world's most precise measurement of a $C\!P$ asymmetry in $B$ meson mixing and is consistent with the Standard Model prediction. The second measurement determines the production asymmetry of $D^{\pm}_s$ mesons, and probes non-perturbative QCD models. It is performed in bins of transverse momentum and pseudorapidity in the kinematic region $2.5< p_{\rm T}<25.0$ GeV and $2.0 < y < 4.5$. The $D^{\pm}_s$ mesons are reconstructed in the $K^{\pm}K^{\mp}\pi^{\pm}$ final state, where the $K^{\pm}K^{\mp}$ pair goes through the $\phi$ resonance. The result is corrected for detection and background asymmetries using similar techniques as for the measurement of $a_{\rm sl}^s$. The resulting value is \begin{align*} A_{\rm P}(D^+_s) &= (-0.48 \pm 0.10 \mathrm{\,(stat)} \pm 0.10\mathrm{\,(syst)})\% \ , \end{align*} which is in agreement with the previous measurement from LHCb. No dependence on the $D^{\pm}_s$ kinematics is found. In addition, a study on the performance of three adhesives for the assembly of vertex modules for the LHCb upgrade is performed and reported in this thesis. These are two liquid glues, Araldite 2011 and Stycast 2850FT, and one double-sided adhesive tape, 3M 9461P, which are all tested for shear strength and thermal conductivity. Stycast 2850FT is proposed to be utilised.