width limit, a standard subtraction method approach will lead to divergent results. In order to illustrate this problem, we consider the example of $t$-channel single top production and decay. One Born amplitude for this process is illustrated in fig. \[fig:ST\].

![Single top $t$-channel production. \[fig:ST\]](ST){width="6cm"}

The final state is composed by a $b$ and $d$ quark, a muon neutrino and an anti-muon. We assume for the sake of illustration a massless $b$ quark. The system comprising the final state $b$ quark, the neutrino and the anti-muon have an invariant mass close to the top mass, becoming identical to the top mass in the zero width limit. Consider now the real contribution obtained by adding gluon radiation to the final state. As illustrated above, in generic subtraction methods, the subtraction counterterms are obtained by factorizing the real phase space in terms of a Born phase space times a radiation phase space. The subtraction term for the collinear singularity corresponding to the final state gluon being collinear to the final $b$ uses a Born phase space where the collinear $b g$ pair is merged into a single $b$. The problem with the resonance is better illustrated in the CS subtraction framework, where 