How are handle small width?

1) Very small width (smaller than 1e-6 times the mass) can lead to numerical precision issue and lead to huge speed down of the code. For this reason, very small width are replaced by a fake width (by default 1e-6 times the mass) to speed up the code and to avoid numerical accuracy issue.
  - The total cross-section is not impacted by the change of the cross-section since the contribution of S-Channel are rescaled by the ratio of the width (which is valid as long as Narrow-Width Approximation holds --which should always be the case for such small width).
  - The BreitWigner shape of the S-Channel resonances would be too large (the width of that shape will be the fake one) and all associated observables will be impacted (but one should expect to have no impact for any experiment)

To desactivate such treatement (or change the threshold where it occurs) you can add the following line in run_card
1e-12 = small_width_treatment

2) Displaced vertex are not similate by default in MG5aMC. You can however activate it via the run_card via the parameter: time_of_flight