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.Differential measurements of particle collisions or decays can provide stringent constraints on physics beyond the Standard Model of particle physics. In particular, the distributions of the kinematical and angular variables that characterise heavy meson multibody decays are non-trivial and can be used to probe this new physics. In the era of high luminosity opened by the advent of the Large Hadron Collider and of Flavor Factories, differential measurements are less and less dominated by statistical precision and require a precise determination of efficiencies that depend simultaneously on several variables and do not factorise in these variables. This article is a reflection on the potential of multivariate techniques for the determination of such multidimensional efficiencies. We carried out two case studies showing that multivariate techniques, such as neural networks, can determine and correct for the distortions introduced by reconstruction and selection criteria in the multidimensional phase space of the decays $ B^{0}\rightarrow K^{*0}(\rightarrow K^{+}\pi^{-})\mu^{+}\mu^{-}$ and $ D^{0}\rightarrow K^{-}\pi^{+} \pi^{+}\pi^{-}$, at the price of a minimal analysis effort. We conclude that this method can already be used for measurements which statistical precision does not yet reach the percent level. With more sophisticated machine learning methods, the aforementioned potential is very promising.

On the potential of multivariate techniques for the determination of multidimensional efficiencies