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

TL;DR

This paper explores the use of multivariate machine learning techniques, specifically neural networks, to accurately determine multidimensional efficiencies in particle decay measurements, improving precision in high-luminosity collider experiments.

Contribution

It demonstrates that multilayer perceptron neural networks can effectively correct for multidimensional efficiency distortions in complex particle decay analyses.

Findings

Neural networks can determine and correct efficiency distortions in multidimensional phase space.

The method requires minimal analysis effort and is suitable for current precision levels.

Potential for more advanced machine learning techniques to further enhance accuracy.

Abstract

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 me- son multibody decays are non trivial and can sign the underlying interaction 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 docu- ment is a reflection on the potential of multivariate techniques for the determination of such multidimensional efficiencies. We carried out two case studies that show that multilayer perceptron 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 and that with more sophisticated machine learning methods, the aforementioned potential is very promising.