On the optimal determination of differential rates in the presence of higher-dimensional operators

When the Standard Model is interpreted as the renormalizable sector of a low-energy effective theory, the effects of new physics are encoded into a set of higher-dimensional operators. These operators potentially deform the shapes of Standard Model differential distributions of final states observable at colliders. We describe a simple and systematic method to obtain optimal estimations of these deformations when using numerical tools, like Monte Carlo simulations. A crucial aspect of this method is minimization of the estimation uncertainty: we demonstrate how the operator coefficients have to be set in the simulations in order to get optimal results. The uncertainty on the interference term turns out to be the most difficult to control and grows very quickly when the interference is suppressed. We exemplify our method by computing the deformations induced by the ${\cal O}_{3W}$ operator in $W^+W^-$ production at the LHC, and by deriving a bound on ${\cal O}_{3W}$ using 8 TeV CMS data.