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The thesis is organized as follows: Chapter 1 describes the theoretical framework of non-leptonic B{sub (s)}{sup 0} {yields} H{sup +}h{prime}{sup -} decays, with a simple overview of the CP violation mechanism within the Standard Model and of the most used phenomenological approaches in the evaluation of strong interaction contributions. The chapter contains also a review of the theoretical expectations and the current experimental measurements along with a discussion about the importance of studying such decays. Chapter 2 contains a general description of the Tevatron collider and of the CDF II detector. Chapter 3 is devoted to the description of the data sample used for the measurement and the method used in extracting the signal from the background. Particular attention is dedicated to the on-line trigger selection, which is crucial to collect a sample enriched in B{sub (s)}{sup 0} {yields} h{sup +}h{prime}{sup -} decays. Chapter 4 shows how the information from kinematics and particle identification was used to achieve a statistical discrimination amongst modes to extract individual measurements. The available resolutions in mass or in particle identification are separately insufficient for an event-by-event separation of B{sub (s)}{sup 0} {yields} h{sup +}h{prime}{sup -} modes. The choice of observables and the technique used to combine them is an important and innovative aspect of the analysis described in this thesis. Chapter 5 is devoted to the accurate determination of the invariant mass lineshape. This is a crucial ingredient for resolving overlapping mass peaks. This chapter details all resolution effects with particular attention at the tails due to the emission of low-energy photons from charged kaons and pions in the final state (FSR). For the first time the effect of FSR has been accurately accounted for in a CDF analysis. Chapter 6 describes how kinematic and PID information, discussed in chap. 4 and chap. 5 were combined in a maximum Likelihood fit to statistically determine the composition of the B{sub (s)}{sup 0} {yields} h{sup +}h{prime}{sup -} sample. This kinematics-PID combined fit has been developed and performed for the first time at CDF in the analysis presented in this thesis and this methodology was later inherited by several other analyses. Chapter 7 is devoted to the study of the isolation variable, which is a crucial handle to enhance the signal-to-background ratio in the off-line selection. It exploits the property that the b-hadrons tend to carry a larger fraction of the transverse momentum of the particles produced in the fragmentation, with respect to lighter hadrons. Since the simulators do not accurately reproduce the fragmentation processes, this chapter is devoted to the study of the control data sample of B{sub (s)}{sup 0} {yields} J/{psi}X decays to probe the characteristics of this variable. Chapter 8 describes an innovative procedure used to optimize the selection to minimize the statistical uncertainty on the quantities one wishes to measure. The procedure is based on the fit of composition described in chap. 6. Chapter 9 reports the results of the fit of composition described in chap. 6 and the cross-checks performed to verify the goodness of the fit of composition. In order to translate the parameters returned from the fit into physics measurements the relative efficiency corrections between the various decay modes need to be applied. Chapter 10 is devoted to the description of these corrections. Chapter 11 describes the measurement of the detector-induced charge asymmetry between positively and negatively charged kaons and pions, due to their different probability of strong interaction in the tracker material using the real data. This allows to extract the acceptance correction factor for the CP asymmetries measurement without any external inputs from the simulation, and to perform a powerful check of whole analysis. Chapter 12 describes the main sources of systematic uncertainties and the method used to evaluate the significance of the results on rare modes. The final results of the measurements and their interpretation are discussed in chap. 13

Measurements of CP asymmetries and branching fractions of two-body charmless decays of B<sup>0</sup> and B$0\atop{s}$ mesons