Study of charmless three-body decays of neutral B mesons with the LHCb spectrometer

This thesis describes an exploratory work on three-body charmless neutral $B$ mesons decays containing either a $K_S$ or $\pi^0$. The events are reconstructed with the LHCb spectrometer installed at Cern (Geneva, CH) recording the proton-proton collisions delivered by the Large Hadron Collider (LHC). The phenomenology of such modes is rich and covers the possibility to measure all angles of the unitarity triangle linked to the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The single example of the $\gamma$ measurement is explored in this document. The LHC accelerator and the most relevant sub-detector elements of the LHCb spectrometer are described in details. In particular, emphasis is given to the calorimetry system for which the calibration and alignment of the PreShower (PRS) of the electromagnetic calorimeter has been performed. We used particles at minimum ionisation deposit for such a task. The calibration results until year 2011 are reported as well as the method of the PS alignment with respect to the tracking system of the spectrometer. A method to discriminate high energy $\pi^0$ and photon is introduced, based on electromagnetic cascade information combined into a multivariate analysis. The strategy to evaluate the performance is given and the tool is applied to the exploratory search of $B \to hh\pi^0$ final states. Additionally, we conducted a similar search for the modes $B_{d,s} \to K_{S}hh$, where $h$ can be either a charged kaon or a pion. The physics reach of such modes lies in the possibility of measuring the $\beta$ and $\beta_s$ CKM angles to be compared to their charmonia extraction. Differences in between these determinations can be the sign of New Physics. The first step of this search is to establish the unobserved modes $B_s \to K_{S}hh$. We report in a fifth of the data 2011 statistics the first observation of the decay channel $B_s \to K_{S}K\pi$.