Dr. Ivan Pedron

Reconstructing distributions from Monte-Carlo computations using orthogonal basis functions

Abstract

Reconstructing kinematic distributions from high-dimensional Monte Carlo integrations is a standard task in high-energy physics, typically performed by binning randomly generated events into histograms. However, this approach often suffers from statistical noise and bin-to-bin fluctuations, especially in higher-order perturbative calculations with local subtractions. We explore an alternative approach, whose main idea is to approximate the target distribution by a weighted sum of orthogonal basis functions whose coefficients are calculated within the Monte-Carlo integration. This yields smooth, continuous representations of the distribution and eliminates bin-to-bin fluctuations. We also demonstrate how the availability of a good approximation to the target distribution, for example the leading-order result, can be exploited to construct an optimized orthonormal basis. We study the performance of this method in both toy-model and real Monte-Carlo settings, applying it to Higgs boson production in weak boson fusion as an example.