Measurements of CP violation in B decays to charmless charged two-body final states at LHCb

This thesis presents the results obtained from the measurements of both the time-integrated (TI) $C\!P$ asymmetries of the $B^0 \rightarrow K^+ \pi^-$ and $B_s^0 \rightarrow \pi^+ K^-$ decays and the time-dependent (TD) $C\!P$ asymmetries of the $B^0 \rightarrow \pi^+ \pi^-$ and $B_s^0 \rightarrow K^+ K^-$ decays. Such measurements have been performed using a data sample corresponding to an integrated luminosity of $3.0~\mathrm{fb}^{-1}$ collected in proton-proton ($pp$) collisions at the centre-of-mass energy of 7-8~TeV at the LHCb experiment during the 2011 and 2012 data taking (Run~1). The final values of the $C\!P$ parameters and asymmetries are: \begin{equation*} \begin{split} C_{\pi^+\pi^-} & = -0.34 \pm 0.06 \pm 0.01, \\ S_{\pi^+\pi^-} & = -0.63 \pm 0.05 \pm 0.01, \\ C_{K^+K^-} & = \phantom{-} 0.20 \pm 0.06 \pm 0.02, \\ S_{K^+K^-} & = \phantom{-} 0.18 \pm 0.06 \pm 0.02, \\ A^{\Delta\Gamma}_{K^+K^-} & = -0.79 \pm 0.07 \pm 0.10, \\ A_{C\!P}(B^0 \rightarrow K^+ \pi^-) & = -0.084 \pm 0.004 \pm 0.003, \\ A_{C\!P}(B^0_s \rightarrow \pi^+ K^-) & = \phantom{-} 0.213 \pm 0.015 \pm 0.007, \\ \end{split} \end{equation*} where the first uncertainty is statistical and the second is systematic. The results are in good agreement with the previous measurements. \\ The values of $C_{\pi^+\pi^-}$, $S_{\pi^+\pi^-}$, $A_{C\!P}(B^0 \rightarrow K^+ \pi^-)$ and $A_{C\!P}(B^0_s \rightarrow \pi^+ K^-)$ are the most precise measurements achieved by a single experiment and the results obtained for $C_{K^+K^-}$, $S_{K^+K^-}$ and $A^{\Delta\Gamma}_{K^+K^-}$ represent the strongest evidence for the TD $C\!P$ violation in the $B^0_s$ meson sector to date. These measurements are published in Physical Review D98[1]. In addition, the preliminary results of the analysis update performed using the data corresponding to an integrated luminosity of $2.0~\mathrm{fb}^{-1}$ collected at the LHCb experiment in $pp$ collisions at the centre-of-mass energy of 13~TeV during the 2015 and 2016 data taking are presented. The values obtained for the $C\!P$ parameters and asymmetries are: \begin{equation*} \begin{split} C_{\pi^+\pi^-} & = -0.375 \pm 0.061, \\ S_{\pi^+\pi^-} & = -0.682 \pm 0.053, \\ C_{K^+K^-} & = \phantom{-}0.124 \pm 0.051, \\ S_{K^+K^-} & = \phantom{-}0.186 \pm 0.052, \\ A^{\Delta\Gamma}_{K^+K^-} & = -0.786 \pm 0.065, \\ A_{C\!P}(B^0 \rightarrow K^+ \pi^-) & = -0.083 \pm 0.003 \pm 0.003, \\ A_{C\!P}(B^0_s \rightarrow \pi^+ K^-) & = \phantom{-}0.244 \pm 0.014 \pm 0.003, \\ \end{split} \end{equation*} where the first uncertainty is statistical and the second is systematic. The statistical precision on the $C\!P$ parameters measured from the TD $C\!P$ asymmetries is expected to be reduced by a relative $30\%$, when the analysis will be completed. The study of the systematic sources of uncertainties has to be finalized and the total uncertainty is expected to be slightly lower than the Run~1 analysis.