dorsal/arxiv
View SchemaOn the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions
| Authors | Kirill Melnikov, Ivan Novikov, Ivan Pedron |
|---|---|
| Categories | |
| ArXiv ID | 2601.10420vv1 |
| URL | https://arxiv.org/abs/2601.10420 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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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.",
"arxiv_id": "2601.10420",
"authors": [
"Kirill Melnikov",
"Ivan Novikov",
"Ivan Pedron"
],
"categories": [
"hep-ph"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "On the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions",
"url": "https://arxiv.org/abs/2601.10420",
"version": "v1"
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