the soft approximations in $d$ dimensions (see for example [[@Mangano:1991jk]]{}).

More recently, fully general formulations of the subtraction method have appeared. The procedure of ref. [[@Catani:1996vz]]{}, known as the CS method, uses local subtraction terms for the $R_s$ cross section. The formulation given in ref. [[@Frixione:1995ms]]{}, known as the FKS method, is instead based upon the more traditional phase space parametrizations used in refs. [[@Ellis:1980wv]]{} and [[@Mele:1990bq]]{}.

The subtraction method and resonances
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When resonances are present, in the zero width limit, the cross section factorizes into the product of production and decay terms. In these cases, a standard subtraction method can be applied independently to the production and decay processes. In fact this was done in refs. [[@Melnikov:2011qx]]{} and [[@Campbell:2012uf]]{} for top production and decay. Problems do arise, however, if finite width effects are fully included, so that also interference among radiation produced in production and decays, or among radiation produced in the decay of different resonances, is included.

On the one hand, the presence of a finite width regulates the singularity associated with the resonance peak, so that, strictly speaking, a subtraction method will formally lead to finite and consistent results. On the other hand, taking the zero 