Reconstruction of two-body B decays in LHCb

The observed dominance of matter over antimatter in the Universe leads to the hypothesis of the Sakharov conditions for the laws of nature. One of them implies the breaking of the charge-parity (CP) symmetry. The violation of the CP symmetry has been observed in several decays of kaons and B mesons and is incorporated in the Standard Model via the CKM matrix, describing the quark transitions in the charged current weak interactions. The Large Hadron Collider (LHC) provides a copious source of bb quark pairs, offering an excellent facility to study CP violation in the B meson system. The LHC is a powerful pp collider, which will accelerate proton bunches in opposite directions in a ring of 27 km circumference. Protons will collide every 25 ns at a center-of-mass energy of 14 TeV. It is foreseen to start operation in 2008. LHCb, one of the four experiments along the LHC ring, is dedicated to the study of CP violation and rare decays in the B meson system. Since bb pairs are mostly produced in a forward cone along the beam axis, LHCb is designed as a single-arm spectrometer, covering a region of 300 mrad and 250 mrad in the horizontal and vertical planes, respectively. The main function of the LHCb tracking system is to efficiently reconstruct charged tracks, to determine primary and secondary decay vertices and to provide particle momentum measurements. This is realized by a Vertex Locator, around the interaction region, a Trigger Tracker, just in front of the magnet and three Tracking Stations, just after the magnet. The particle identification system provides \pi/K separation, performed by two RICH detectors, electron, photon and hadron identification, accomplished by the calorimeters system, and muon identification with dedicated muon chambers. The Tracking Stations (T-stations) measure the momenta of charged particles. They cover a surface-area of about 6 × 5 m2. Over this area there is a large variation in the particle flux. In order to deal with this, the innermost part (IT) is covered with silicon strips, while the outer part (OT) is covered with straw tube drift cells. The OT serves to reconstruct tracks with a nominal momentum resolution (Deltap/p) of about 0.5% in the momentum region of 2 to 100 GeV. The OT layers in the T stations consist of modules. Each mechanical module has two separated detector halves, each of them contains again two mono-layers of straw tubes. The detector efficiency and resolution have been measured in a test beam: a resolution better than 200 \mu m and an average cell efficiency E_{cell} of 98% have been found. The performance of the LHCb detector, and of the OT in particular in this thesis, is estimated through a detailed simulation and reconstruction program. A realistic event simulation and an accurate description of the detector are needed in order to develop and test the reconstruction program under realistic circumstances. Several effects are included in the simulation of the OT detector response (digitization). The single cell efficiency and the resolution are described according to the measurements in the test beam, as is the background hit rate due to cross talk (5%), and random noise (10 kHz). Understanding the alignment of the Outer Tracker detector modules is essential in the track reconstruction. A particle passing through a misaligned detector, if fitted assuming the uncorrected geometry, potentially causes wrong hits to be assigned to the track and certainly leads to a deteriorated momentum resolution. The misalignments of the Outer Tracker system resulting from the finite accuracy of the detector production, installation, positioning and survey have to be corrected for in the offline software. Here a least-squares fit method based on the "Millepede" package is used. The key importance of an accurate alignment is demonstrated in the physics studies of the B0_{s} -> h^{+}h'^{-} and of the B0_{s} -> \mu^{+}\mu^{-} decays. In two-body B decays, the uncertainty on the mass reconstruction is dominated by the momentum resolution of the decay products. Among the several sources of uncertainties affecting the measurement of the momenta of the decay particles, an important role is played by misalignments of the tracking system. The impact of a misaligned OT detector and a corresponding deteriorated momentum resolution is studied in the analysis of B0_{s} -> h^{+}h'^{-} decay events. This is particularly crucial in the study of the B0s -> \pi^{+}K^{-} decay events, where a deteriorated mass resolution does not allow them to be separated from the \overline{B^{0}_{d}} -> \pi^{+}K^{-} decay events. The combined measurement of the time-dependent CP asymmetries of B^{0}_{d} -> \pi^{+}\pi^{-} and B^{0}_{s} -> K^{+}K^{-} decays leads to a determination of the Unitarity Triangle angle gamma, up to U-spin flavour-symmetry breaking corrections. The extraction of gamma has been performed with an UTFit Bayesian approach in various U-spin symmetry scenarios and using as input different values of mass resolutions, corresponding to different OT misalignments. In all the Uspin symmetry scenarios considered, given the correspondence between mass resolution and OT-misalignments, a maximum deterioration of approximately 30% of the LHCb sensitivity to gamma is obtained for a misalignment value of 1.0 [mm/mrad], corresponding to a scenario in which the stations T1 and T3 have been translated of 1.0 mm in X,Y,Z and at the same time rotated by 1.0 mrad around the X,Y,Z axis in opposite directions. Flavor Changing Neutral Currents (FCNC) are forbidden in the Standard Model at the tree level by the GIM mechanism. As a consequence FCNC only appear in the Standard Model when 2nd order loop diagrams are considered. Therefore decays which depend on FCNC, so-called rare decays, are very sensitive to "new physics" phenomena, where, in addition, a strong dependence on virtually exchanged particles might be observed. In particular the B0s -> \mu^{+}\mu^{-} Standard Model branching ratio can be enhanced by one to three orders of magnitude according to scenarios implying the existence of supersymmetric particles. Assuming the Standard Model branching ratio, the LHCb sensitivity to the B0s -> \mu^{+}\mu^{-} decay has been estimated to be 4.7 ± 0.3 sigma with five years of data taking at nominal luminosity.