A generalized statistical model for fits to parton distributions

Abstract

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF fitting groups encounter is the presence of tension in data sets that appear to pull the fits in different directions. In other words, the best fit depends on the choice of data set. Several methods to capture the uncertainty in PDFs in presence of seemingly inconsistent fits have been proposed and are currently in use. These methods are important to ensure that uncertainty in PDFs are not underestimated. Here we propose a novel method for estimating the uncertainty by introducing a generalized statistical model based on Bayesian Hierarchical models which is implemented via the Gaussian Mixture Model (GMM). The methodology is inspired by unsupervised machine learning techniques and is closely related to the statistical methods of Ensemble learning and Bayesian model averaging. Using a toy model of PDFs, we demonstrate how the GMM can be used to faithfully reconstruct the likelihood associated with PDF fits, which can in turn be used to accurately determine the uncertainty on PDFs, especially in the presence of tension in the fitted data sets. We further show how this statistical model reduces to the usual chi-squared likelihood function for a consistent data set and provide measures to optimize the number of Gaussians in the GMM.

52 pages, 14 figures. Updated to match journal version. Includes new appendices with a pedagogical examples and discussion

References in corpus (31)

• Parton distributions for the LHC
• New parton distributions for collider physics
• Parton distributions in the LHC era: MMHT 2014 PDFs
• Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP
• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• The CT10 NNLO Global Analysis of QCD
• Using stacking to average Bayesian predictive distributions
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• Parton Distribution Functions, ${\alpha }_s$ and Heavy-Quark Masses for LHC Run II
• The Path to Proton Structure at One-Percent Accuracy
• Parton distributions and lattice QCD calculations: a community white paper
• Precision measurement and interpretation of inclusive $W^{+}$, $W^{-}$ and $Z/{\gamma }^{\ast }$ production cross sections with the ATLAS detector
• Bayesian model averaging for analysis of lattice field theory results
• Measurement of the W Boson Mass with the D0 Detector
• PDF reweighting in the Hessian matrix approach
• Measurement of the W boson mass
• Evidence for intrinsic charm quarks in the proton
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Hadron structure in high-energy collisions
• Global analysis of electroweak data in the Standard Model
• Improved W boson mass measurement with the D0 detector
• Improved information criteria for Bayesian model averaging in lattice field theory
• Compatibility and combination of world W-boson mass measurements
• Parton distributions need representative sampling
• Measurement of the W-boson mass and width with the ATLAS detector using proton-proton collisions at $\sqrt{s}$ = 7 TeV
• Statistical Models with Uncertain Error Parameters
• Model averaging approaches to data subset selection
• Alternative to the application of PDG scale factors
• Connected and Disconnected Sea Partons from CT18 Parametrization of PDFs
• Model for the curvature response of the CDF II drift chamber