Time alignment of the electromagnetic and hadronic calorimeters, reconstruction of the $B\rightarrow D^{-}\rho(770)^{+}, B_{s}\rightarrow D_{s}^{-}\rho(770)^{+}$ and $B_{s}\rightarrow D_{s}^{-}K^{*+}(892)$ decay channels with the LHCb detector

This thesis has been performed in the framework of the LHCb experiment installed on the LHC proton-proton collider at CERN. First, we have developed an asymmetry-based method to time align both the electromagnetic (ECAL) and hadronic (HCAL) calorimeters. We have shown that with 450 GeV beams and without the magnetic field 55 000 minimum bias events are necessary to time align, with a precision of 0.5 ns, 84 $\%$ of the ECAL cells and 96 $\%$ of the HCAL cells. During the commissioning we have analyzed over a million cosmic events and checked that the internal time alignment of the ECAL and HCAL is better than 1 ns. We have adjusted the relative time alignment between the ECAL and the HCAL to 2 ns. On 10 $^{th}$ of September 2008, the LHC delivered one hour of beam. The interaction between a collimator located upstream of LHCb and the beam leads to the production of hadronic showers, detected in the HCAL. We have shown that the global time alignment of the HCAL and the LHC clocks is about 0.8 ns. We have studied the $B_{d}\rightarrow D^{-}\rho(770)^{+}$, $B_{s}\rightarrow D_{s}^{-}\rho(770)^{+}$ et $B_{s}\rightarrow D_{s}^{-}K^{*+}(892)$ decay modes. All three modes have a neutral pion in the final state. We developed a method that selects signal events and minimizes the $b\bar{b}$ background. With a nominal year of data, we expect 450 000 events for the $B_{d}\rightarrow D^{-}\rho(770)^{+}$ mode, 71 000 events for the $B_ {s}\rightarrow D_{s}^{-}\rho(770)^{+}$ mode and 1300 events for the $B_{s}\rightarrow D_{s}^{-}K^{*+}(892)$ mode, with a background over signal fraction varying between 1.6 and 6.