Determination of proton PDF uncertainties with Markov chain Monte Carlo

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Risse, Peter, Derakhshanian, Nasim, Jezo, Tomas, Kovarik, Karol, Kusina, Aleksander
Format: Preprint
Publié: 2025
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866914427063762944
author Risse, Peter
Derakhshanian, Nasim
Jezo, Tomas
Kovarik, Karol
Kusina, Aleksander
author_facet Risse, Peter
Derakhshanian, Nasim
Jezo, Tomas
Kovarik, Karol
Kusina, Aleksander
contents We present an analysis of parton distribution functions (PDFs) of the proton using Markov Chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes' theorem and thus provides a means to directly sample the underlying probability distribution - in this case the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, $W$ and $Z$ boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing e.g. to account for non-Gaussianity or inconsistencies of data sets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the $Δχ^2$ value corresponding to a given confidence level in the sample, which can in turn be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.
format Preprint
id arxiv_https___arxiv_org_abs_2510_16158
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Determination of proton PDF uncertainties with Markov chain Monte Carlo
Risse, Peter
Derakhshanian, Nasim
Jezo, Tomas
Kovarik, Karol
Kusina, Aleksander
High Energy Physics - Phenomenology
We present an analysis of parton distribution functions (PDFs) of the proton using Markov Chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes' theorem and thus provides a means to directly sample the underlying probability distribution - in this case the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, $W$ and $Z$ boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing e.g. to account for non-Gaussianity or inconsistencies of data sets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the $Δχ^2$ value corresponding to a given confidence level in the sample, which can in turn be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.
title Determination of proton PDF uncertainties with Markov chain Monte Carlo
topic High Energy Physics - Phenomenology
url https://arxiv.org/abs/2510.16158