Convolution Formula and Finite W Boson Width Effects in Top Quark Width Received Day Month Year Revised Day Month Year

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 i ¯ f j 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.