On the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913145687113728 |
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| author | Melnikov, Kirill Novikov, Ivan Pedron, Ivan |
| author_facet | Melnikov, Kirill Novikov, Ivan Pedron, Ivan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10420 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions Melnikov, Kirill Novikov, Ivan Pedron, Ivan High Energy Physics - Phenomenology 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. |
| title | On the reconstruction of kinematic distributions computed with Monte Carlo methods using orthogonal basis functions |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2601.10420 |