CP violation studies on the B0 -> DK*0 decays and hadronic trigger performance with the LHCb detector at CERN

In the Standard Model of particle physics, the Cabibbo-Kobayashi-Maskawa (CKM) mechanism describes the quark mixing effect. The CKM $\gamma$ angle is one of the parameters of the Standard Model that are known less accurately. Direct measurements give an uncertainty of around $15^{\circ}$, large with respect to the uncertainty on the value extracted from global fits, of $3^{\circ}$. In order to test the Standard Model consistency, the $\gamma$ angle needs to be measured precisely. This can be done using processes at the tree-level, where only Standard Model contributions are expected, or using processes involving loop diagrams, which can be sensitive to physics beyond the Standard Model. Differences in the $\gamma$ measurement from tree and loop diagrams would be an indication of new physics. This thesis presents the first measurement of the $CP$ observables in the $\overline{B}^0 \to D\overline{K}^{*0}$ decay. Sensitivity to $\gamma$ arises from the interference of the $b \to u$ mediated amplitude with the $b \to c$ one, at the tree-level. The $CP$ asymmetry of the $\overline{B}^0 \to [K^+K^-]_D\overline{K}^{*0}$ mode and the partial width ratio of this channel with respect to $\overline{B}^0 \to [K^-\pi^+]_D\overline{K}^{*0}$ are measured using 1fb$^{-1}$ of data collected by the LHCb experiment in 2011, \begin{align} A^{KK}_{d} &= -0.452 ~ ^{+0.228}_{-0.230} \pm 0.025 = A_{CP+}, \nonumber\\ R^{KK}_{d} &= \phantom{-}1.360 ~ ^{+0.366}_{-0.319} \pm 0.075 = R_{CP+}.\nonumber \end{align} The $CP$ asymmetry of the suppressed $\overline{B}^0 \to [K^+\pi^-]_D\overline{K}^{*0}$ mode and the partial width ratio with respect to the favoured $\overline{B}^0 \to [K^-\pi^+]_D\overline{K}^{*0}$ are measured using the total $3~\mathrm{fb}^{-1}$ of data collected in 2011 and 2012, \begin{align} A^{sup}_{d} &= -0.094 ~ ^{+0.303}_{-0.318} = A_{ADS}, \nonumber\\ R_d &= \phantom{-}0.075 ~ ^{+0.023}_{-0.022} = R_{ADS}. \nonumber \end{align} In addition, the studies performed on the hardware hadronic trigger of the LHCb experiment are also presented