Width Effects on Near Threshold Decays of the Top Quark t-> cWW,cZZ and of Neutral Higgs Bosons

The nonzero widths of heavy particles become significant when they appear in the final state of any decay occurring just around its kinematical threshold. To take into account such effects, a procedure, called the convolution method, was proposed by Altarelli, Conti and Lubicz. We expand their study which included only threshold effects for t-> bWZ in the standard model. We discuss finite width effects in the three body decays t-> cWW,cZZ and A^0(h^0)->tbW in the type III version of a two Higgs doublet model. In particular, we find a substantial enhancement in the decay t->cZZ, which brings its branching ratio to BR(t->cZZ)~10^-3, and in the decay A^0->tbW, which, unlike the h^0 case, becomes competitive with the A^0 two-body decay modes.