B physics studies at the ATLAS experiment

This thesis focuses on the study of the $CP$ violation and $B$ meson lifetime properties. The Standard Model predicts the $CP$ violating mixing phase $\phi_s$ to be very small and its theoretical value is very well constrained, while any measured deviations from the Standard Model value can indicate New Physics not described by the Standard Model. The first analysis described in this thesis is devoted to the $CP$ violation in decays of $B_s^0 \to J/\psi \phi$. This measurement was performed using $80.5~\mathrm{fb}^{-1}$ of the proton--proton collisions at a centre-of-mass energy of $\sqrt{s}=13$~TeV at the Large Hadron Collider recorded by the ATLAS detector. This analysis uses a precise determination of the initial flavour tagging probability using the decays of $B^\pm \to J/\psi K^\pm$. The results of the $CP$ violation phase and $B_s^0$ lifetime properties were combined with the previous ATLAS measurements at a centre-of-mass energy of 7 and 8~TeV. The combined results agree with the Standard Model and they are: \begin{alignat*}{4} \phi_s &= \pSfitCombi\phantom{0} && ~ \pm ~ \pSstatCombi ~ &&\mathrm{(stat.)} ~\pm ~ \pSsystCombi\phantom{0} ~ &&\mathrm{(syst.)}~\mathrm{rad,} \\ \Delta\Gamma_s &= \phantom{\ensuremath{-}}\DGfitCombi &&~\pm~ \DGstatCombi ~ &&\mathrm{(stat.)} ~\pm ~\DGsystCombi ~&&\mathrm{(syst.)}~\mathrm{ps}^{-1}, \\ \Gamma_s &= \phantom{\ensuremath{-}}\GSfitCombi &&~\pm~ \GSstatCombi ~ &&\mathrm{(stat.)} ~ \pm ~\GSsystCombi ~&&\mathrm{(syst.)}~\mathrm{ps}^{-1}. \end{alignat*} The second analysis presented in this thesis focuses on the measurement of the $B^0$ effective lifetime using $B^0 \to J/\psi (\mu^+\mu^-) K^{*0} (\pi^\pm K^\mp)$ decays in the $139~\mathrm{fb}^{-1}$ data sample of $pp$ collisions collected with the ATLAS detector during the 13~TeV LHC run between years 2015 and 2018. The extracted results are \begin{alignat*}{5} \tau_{B^0} &= 1.5174 && ~ \pm ~ 0.0012 ~ &&\mathrm{(stat.)} ~\pm ~ 0.0016 ~ &&\mathrm{(syst.)} ~ \mathrm{ps}, \\ \Gamma &= 0.6586 && ~ \pm ~ 0.0005 ~ &&\mathrm{(stat.)} ~\pm ~ 0.0006 ~ &&\mathrm{(syst.)}~ \pm ~ 0.0038 ~\textrm{(ext.)} ~ \mathrm{ps}^{-1}. \end{alignat*} Combining this value with the average decay width $\Gamma_s$, their ratio is $$ \frac{\Gamma }{\Gamma_s } = 0.9825 \pm 0.0022 ~\textrm{(stat.)} \pm 0.0028 ~\textrm{(syst.)} \pm 0.0057 ~\textrm{(ext.)}. $$ The lifetime and $\Gamma$ values show perfect agreement with the world average values and theoretical predictions. The $3\sigma$ tension of the $\Gamma/\Gamma_s $ ratio is driven by the tension of the $\Gamma_s$.