in the limit $\Gamma \rightarrow 0$. It is also clear that, in order to overcome this problem, one must devise a subtraction method such that the resonance mass is the same in the real and subtraction terms when approaching the resonance peak even when the resonance is off-shell by an amount greater than its width.

NLO+PS and resonances
---------------------

If we plan to use an NLO calculation with an interface to a shower generator (NLO+PS from now on), further problems arise due to the resonance treatment.

In the method [@Frixione:2002ik], one should consider the recoil scheme used by the Shower Monte Carlo to build radiation from a decaying resonance and construct the MC counterterms accordingly.

In the method [@Nason:2004rx; @Frixione:2007vw; @Alioli:2010xd], one first computes the inclusive cross section for the production of an event with a given underlying Born configuration. Radiation is then generated according to a Sudakov form factor with the following form: $$\Delta (p_T^2) = \exp \left[ - \int \frac{R (\Phi_B, \Phi_{{\ensuremath{\operatorname{rad}}}})}{B
  (\Phi_B)} \theta (k_T (\Phi_{{\ensuremath{\operatorname{rad}}}}) - p_T) {\mathrm{d}}\Phi_{{\ensuremath{\operatorname{rad}}}}
  \right] .$$ The mapping of the real phase space into a product of an underlying Born times a radiation phase space is the same used in the NLO subtraction 