Towards a measurement of the angle $\gamma$ of the Unitarity Triangle with the LHCb detector at the LHC (CERN): calibration of the calorimeters using an energy flow technique and first observation of the $B^0_s \to \overline{D}^0 \overline{K}^{*0}$ decay

The present status on the determination of the angle $\gamma$ of the Cabibbo-Kabayashi-Maskawa Unitary Triangle is statistically limited by the rarity of $b \to u$ transitions. The obtained precision combining results from the BABAR and BELLE experiments is close to 10°. The LHCb experiment at the LHC has a strong potential to reduce the uncertainty on this CP violation parameter, especially through the $B^0 \to D^0 K^{*0}$ decay, one of the key channels for this measurement. The $D^0 \to K^{\pm}\pi^{\mp}$, $D^0 \to K^{\pm}\pi^{\mp}\pi^0$ and $D^0 \to K^{\pm}\pi^{\mp}\pi^+\pi^-$ decays are studied in this thesis. Decays involving $\pi^0$ require an accurate energy calibration of electromagnetic calorimeters. An inter-calibration technique based on the energy flow allows to obtain the 1.5 % level, the absolute scale being obtained from independent methods studied elsewhere. The determination of the $B^0_s \to \overline{D}^0 \overline{K}^{*0}$ decay branching ratio, first step towards a measurement of CP violation in the $B^0 \to D^0 K^{*0}$ channel, is performed relatively to the $B^0 \to \overline{D}^0 \rho^0$ decay. The final result, obtained with 36 pb$^{-1}$ of data collected by LHCb in 2010 is dominated by the statistical uncertainty: \begin{align} \frac{\mathcal{B}\left(\overline{B}_s^0 \rightarrow D^0 K^{*0}\right)}{\mathcal{B}\left(B^0 \rightarrow \overline{D}^0 \rho^0 \right)} = 1.48\pm 0.34\textrm{ (stat)} \pm 0.15\textrm{ (syst)} \pm 0.12 \left(f_d/f_s\right) \end{align}