Study of $b$-quark Processes Using the ATLAS Detector

This thesis focuses on three topics related to the $CP$-violation measurement in the $B_s^0\rightarrow J/\psi\phi$ channel made by the B-Physics working group at the ATLAS experiment. The first analysis is a measurement of the $CP$-violation phase $\phi_s$ in the $B_s^0\rightarrow J/\psi \phi$ channel. This analysis was performed on the $pp$ collisions at centre-of-mass energy $\sqrt{s}=13~\mathrm{TeV}$ collected by the ATLAS experiment with integrated luminosity of $80.5~\mathrm{fb}^{-1}$. The obtained results are statistically combined with the previous ATLAS measurements at centre-of-mass energy $7~\mathrm{TeV}$ and $8~\mathrm{TeV}$. The observed values of the most important $CP$-violation parameters are: $$\phi_s = -0.087 \pm 0.037\mathrm{(stat.)}\pm 0.019\mathrm{(syst.)} \mathrm{rad}$$ $$\Delta\Gamma_s = 0.064 \pm 0.004\mathrm{(stat.)}\pm 0.002\mathrm{(syst.)} \mathrm{ps}^{-1}$$ $$\Gamma_s = 0.670 \pm 0.001\mathrm{(stat.)}\pm 0.002\mathrm{(syst.)} \mathrm{ps}^{-1}$$ All measurements agree with the Standard Model predictions. The second analysis is a measurement of $B^\pm \rightarrow J/\psi K^\pm$ and $B_d^0 \rightarrow J/\psi K^{*0}$ lifetimes. This analysis serves as a benchmark measurement to validate the precision of the lifetime corrections applied on the $B_s^0$ events and the performance of the B-Physics triggers. The last analysis is devoted to the search for a structure in the $B_s^0\pi^\pm$ invariant mass spectrum particularly the search for the resonance $X(5568)$ which is tetra-quark candidate. The upper limit on the number of signal events $N(X)$ and on its production rate relative to $B_s^0$ mesons $\rho_X$ were measured since no statistically significant signal was observed. The measured limits are $N(X) < 382$ and $\rho_X < 0.015$ for $p_\mathrm{T}(B_s^0 ) > 10~\mathrm{GeV}$ and $N (X) < 356$ and $\rho_X < 0.016$ for $p_\mathrm{T} (B_s^0 ) > 15~\mathrm{GeV}$. The ATLAS result is consistent with the results from other LHC experiments.