Convolution formula and finite W boson width effects in the top quark width

Abstract

In the standard model, the top quark decay width \Gamma_t is computed from the exclusive t -> bW decay. We argue in favor of using the three body decays t-> bf_i\bar{f}_j to compute \Gamma_t 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 Gamma_t=\Gamma(t-> bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of \Gamma_t are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher order radiative corrections.