CONVOLUTION FORMULA AND FINITE W BOSON WIDTH EFFECTS IN TOP QUARK WIDTH

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 [Formula: see text] 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 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.