Measurement of branching fractions of B decays to K₁(1270)π and K₁(1400)π and determination of the CKM angle α from B⁰→ a₁(1260)^± π^∓

In the Standard Model, CP violation in weak interactions involving quarks is parameterized by an irreducible complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing-matrix. The precise determination of the CKM elements is a necessary ingredient for a stringent test of the Standard Model predictions, and is a crucial input for reducing the theoretical error in many New Physics searches with flavor, e.g., in the kaon sector. The unitarity of the CKM matrix is typically expressed as a triangle relationship among its parameters, where the area of the so-called Unitarity Triangle visually depicts the amount of asymmetry between the decays of B particles and their antimatter counterparts. In the past few years, the BABAR and Belle experiments have been able to measure all three angles of the triangle from CP asymmetry measurements. The first asymmetry measurements in B particle decays, about ten years ago, allowed to determine {beta}, which is now known to better than 5% precision. The angles {alpha} and {gamma}, measured in much rarer processes, required several years of data taking before analyses could yield reliable answers. A remarkable feature is that the direct measurement of the angles of the Unitarity Triangle generates an area that is consistent with the area predicted by measurement of the sides. In this thesis we have presented the branching fraction measurements of charged and neutral B meson decays to K{sub 1}(1270){pi} and K{sub 1}(1400){pi}, obtained from a data sample of 454 million {Upsilon}(4S) {yields} B{bar B} events. This analysis is particularly challenging from the experimental side since the branching fractions involved are very low, at the level of 10{sup -6} - 10{sup -7}, and the signal is characterized by the simultaneous presence of two overlapping resonances, which exhibit sizeable interference effects. The combined K{sub 1}(1270){pi} and K{sub 1}(1400){pi} signal is therefore modeled with a K-matrix formalism, which accounts for the effects of interference between the K{sub 1}(1270) and K{sub 1}(1400) mesons by introducing two effective parameters. The model is derived from the analysis, performed by the ACCMOR Collaboration, of the diffractive production of strange mesons