Study of charmless $B_{(s)}$ meson decays involving $\eta'$ and $\phi$ intermediate states at the LHCb experiment

LHCb is one of the four main experiments located at the Large Hadron Collider (LHC) at CERN, and has collected about 3 ${\rm fb}^{-1}$ of proton-proton collisions at $\sqrt{s}= 7$ TeV and 8 TeV between December 2009 and December 2012. Designed for the study of $B$-meson decays and for precision $CP$-violation measurements, the LHCb detector requires a high resolution vertex reconstruction, a precise measurement of the charged particle's momentum and an excellent particle identification. In this thesis, a study of the LHCb magnetic field map and two physics analyses are presented. Based on the magnetic field measurements collected during a dedicated campaign in February 2011, the magnetic field map is corrected for mis-alignments, considering global translations and rotations. A more reliable mapping of the field is provided, and is used for the LHCb event reconstruction since June 2011. As a consequence of this study, the mass resolution is improved, and a better agreement between the software alignment and the survey measurements of the tracking stations is obtained. The physics analyses presented in this thesis are focused on the study of charmless $B$ decays, and exploit the 1 ${\rm fb}^{-1}$ of data at $\sqrt{s}=7$ TeV and the 2 ${\rm fb}^{-1}$ of data at $\sqrt{s}=8$ TeV collected in 2011 and 2012, respectively. Because of the tiny $b \to u$ tree and $b \to s(d)$ penguin transitions, and the large number of unexplored channels, charmless $B$ decays constitute a very promising sector for new physics discovery, both in branching fraction measurements of penguin dominated decays, and in $CP$ violation measurements. The first analysis, performed with the 7 TeV data, is dedicated to the search of the rare $B^{\pm}\to \phi \pi^{\pm}$ decay and to the measurement of the $B^{\pm}\to \phi K^{\pm}$ $CP$ asymmetry. In both cases, a deviation from the Standard Model predictions would be an indication of new physics. The best upper limit on the $B^{\pm}\to \phi \pi^{\pm}$ and the most precise $B^{\pm}\to \phi K^{\pm}$ $CP$ asymmetry are obtained: \begin{equation} \mathcal{B}(B^{\pm}\to \phi \pi^{\pm})< 1.55 (1.80) \times 10^{-7} \mbox{at 90\% (95\%) CL} \, , \end{equation} and \begin{equation} \mathcal{A}(B^{\pm}\to \phi K^{\pm})= (2.2\pm2.1{\rm(stat)} \pm 0.7{\rm(syst)}\pm0.6(J\psi K^{\pm})) \times 10^{-2} \, , \end{equation} where the last uncertainty accounts for the uncertainty on the knowledge of the $B^{\pm}\to J/\psi K^{\pm}$ charge asymmetry, used as reference. Both measurements are compatible with the theoretical predictions, which are in the range $(0.5-6.0)\times10^{-8}$ for the $B^{\pm}\to \phi \pi^{\pm}$ branching fraction and of $1-2\%$ with uncertainty of few percent for the $B^{\pm}\to \phi K^{\pm}$ $CP$ asymmetry. An update of the $B^{\pm}\to \phi K^{\pm}$ $CP$ asymmetry is performed including the 2012 data leading to a further improvement in precision: \begin{equation} \mathcal{A}^{CP}(B^{\pm}\to \phi K^{\pm})= (1.7\pm 1.1{\rm(stat)} \pm 0.2{\rm(syst)}\pm 0.6(J\psi K^{\pm})) \times 10^{-2} \, . \end{equation} A second analysis is described in this thesis, which aims at the study of $B^{\pm}$ and $B^{0}_{s}$ decays with $\eta'$ resonances in the final state, exploiting the full 2011 and 2012 statistics. Two modes are investigated: the $B^0_s\to \eta' \eta'$ mode, not observed yet, which branching fraction is predicted in the range $(14-50)\times10^{-6}$, and the $B^{\pm}\to \eta' K^{\pm}$ mode, used as reference channel for the $B^0_s\to \eta' \eta' $ search, and for which the $CP$ asymmetry is also measured. All the $\eta'$ resonances are reconstructed in the $\pi^{+}\pi^{-}\gamma$ final state, which introduces the additional challenge of identifying and reconstructing photons in the LHCb hadronic environment. As a result, the $B^0_s\to \eta' \eta'$ decay is observed for the first time with a significance of $6.4$, and its branching ratio is measured to be: \begin{equation} \mathcal{B}(B^0_s\to\eta'\eta') = (3.31\, \pm 0.64{\rm (stat)} \pm 0.28{\rm (syst)}\pm 0.12(B^{\pm}\to \eta' K^{\pm}))\times 10^{-5} \,. \end{equation} Finally, the most precise measurement of the $B^{\pm}\to \eta' K^{\pm}$ $CP$ asymmetry is obtained: \begin{equation} \mathcal{A}^{CP}(B^{\pm}\to \eta' K^{\pm})= (-0.2\pm 1.2{\rm(stat)} \pm 0.1{\rm(syst)}\pm 0.6(J\psi K^{\pm})) \times 10^{-2} \end{equation} compatible with the current PDG average, $\mathcal{A}^{CP}(B^{\pm}\to \eta' K^{\pm})=0.013\pm0.017$.