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On the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions
by Kirill Melnikov, Ivan Novikov, Ivan Pedron
Submission summary
| Authors (as registered SciPost users): | Ivan Pedron |
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| Preprint Link: | https://arxiv.org/abs/2601.10420v1 (pdf) |
| Date submitted: | Jan. 28, 2026, 3:50 p.m. |
| Submitted by: | Ivan Pedron |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
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Abstract
Reconstruction of one-dimensional kinematic distributions from calculations based on high-dimensional Monte-Carlo integration is a standard problem in high-energy physics. Traditionally, this is done by collecting randomly-generated events in histograms. In this article, 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 using the Monte-Carlo integration. This method has the advantage of directly yielding smooth approximations to target distributions. Furthermore, in the context of high-order perturbative calculations with local subtractions, it eliminates the so-called bin-to-bin fluctuations, which often severely affect the quality of conventional histograms. We also demonstrate that the availability of a high-quality approximation to the target distribution, for example the leading-order result in the perturbative expansion, can be exploited to construct an optimized orthonormal basis. We compare the performance of this method to conventional histograms in both toy-model and real Monte-Carlo settings, applying it to Higgs boson production in weak boson fusion as an example.