We present a systematic study of exclusive charmless nonleptonic two-body B decays including axial-vector mesons in the final state. We calculate branching ratios of B → P A, V A and AA decays, where A, V and P denote an axial-vector, a vector and a pseudoscalar meson, respectively. We assume naive factorization hypothesis and use the improved version of the nonrelativistic ISGW quark model for form factors in B → A transitions. We include contributions that arise from the effective ∆B = 1 weak Hamiltonian H ef f . The respective factorized amplitude of these decays are explicitly showed and their penguin contributions are classified. We find that decayshave branching ratios of the order of 10 −5 . We also study the dependence of branching ratios for B → K1P (V, A) decays (K1 = K1(1270), K1(1400)) with respect to the mixing angle between KA and KB.

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In the standard model, the top quark decay width Γt is computed from the exclusive t → bW decay. We argue in favor of using the three body decays t → bf ifj to compute Γt as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula (CF) commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Γt = Γ(t → bW ) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of Γt are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher order radiative corrections.

We update the determination of |V us | using semielectronic and semimuonic decays of K mesons. A modest improvement of 15% with respect to its present value is obtained for the error bar of this matrix element when we combine the four available semileptonic decays. The combined effects of long-distance radiative corrections and nonlinear terms in the vector form factors can decrease the value of |V us | by up to 1%. Refined measurements of the decay widths and slope form factors in the semimuonic modes and a more accurate calculation of vector form factors at zero momentum transfer can push the determination of |V us | at a few of percent level.