A Stress Test of Global PDF Fits: Closure Testing the MSHT PDFs and a First Direct Comparison to the Neural Net Approach

Abstract

We present a first global closure test of the fixed parameterisation (MSHT) approach to PDF fitting. We find that the default MSHT20 parameterisation can reproduce the features of the input set in such a closure test to well within the textbook uncertainties. This provides strong evidence that parameterisation inflexibility in the MSHT20 fit is not a significant issue in the data region. We also present the first completely like--for--like comparison between two global PDF fits, namely MSHT and NNPDF, where the only difference is guaranteed to be due to the fitting methodology. To achieve this, we present a fit to the NNPDF4.0 data and theory inputs, but with the MSHT fixed parameterisation. We find that this gives a moderately, but noticeably, better fit quality than the central NNPDF4.0 fits, both with perturbative and fitted charm, and that this difference persists at the level of the PDFs and benchmark cross sections. The NNPDF4.0 uncertainties are found to be broadly in line with the MSHT results if a textbook $T^2=1$ tolerance is applied, but to be significantly smaller if a tolerance typical of the MSHT20 fit is applied. This points to an inherent inconsistency between these approaches. We discuss the need for an enlarged tolerance criterion in global PDF fits in detail, and demonstrate the impact of data/theory inconsistencies in the closure test setting; namely, these do not lead to any increase in the $T^2=1$ PDF uncertainty. We also investigate the impact of restricting the PDF parameterisation to have fewer free parameters than the default MSHT20 case, and find this can be significant at the level of both closure tests and the full fit.

102 pages, 54 figures, 10 tables. Version accepted for publication in EPJC. Many changes and updates, including expansion of statistical estimators and further discussion in Section 3, and reorganisation of Section 7

References in corpus (18)

• Parton distributions for the LHC
• Parton distributions in the LHC era: MMHT 2014 PDFs
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs
• Evidence for intrinsic charm quarks in the proton
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• Extended Parameterisations for MSTW PDFs and their effect on Lepton Charge Asymmetry from W Decays
• Inclusive Production Cross Sections at N3LO
• Bayesian Approach to Inverse Problems: an Application to NNPDF Closure Testing
• EKO: Evolution Kernel Operators
• The persistent nonperturbative charm enigma
• Positivity and renormalization of parton densities
• Towards parton distribution functions with small-$x$ resummation: HELL 2.0
• Deuteron Uncertainties in the Determination of Proton PDFs
• Parton distributions need representative sampling
• Simultaneous CTEQ-TEA extraction of PDFs and SMEFT parameters from jet and $t\bar{t}$ data
• On the determination of uncertainties in parton densities

Cited by in corpus (1)

• Assessing the Impact of Fitting Methodology at aN${}^3$LO with FPPDF: an Open Source Tool for Extracting Parton Distribution Functions in the Hessian Approach