Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs

Abstract

We present the first global analysis of parton distribution functions (PDFs) at approximate N${}^3$LO in the strong coupling constant ${\alpha }_s$, extending beyond the current highest NNLO achieved in PDF fits. To achieve this, we present a general formalism for the inclusion of theoretical uncertainties associated with the perturbative expansion in the strong coupling. We demonstrate how using the currently available knowledge surrounding the next highest order (N${}^3$LO) in ${\alpha }_s$ can provide consistent, justifiable and explainable approximate N${}^3$LO (aN${}^3$LO) PDFs. This includes estimates for uncertainties due the the currently unknown N${}^3$LO ingredients, but also implicitly some missing higher order uncertainties (MHOUs) beyond these. Specifically, we approximate the splitting functions, transition matrix elements, coefficient functions and $K$-factors for multiple processes to N${}^3$LO. Crucially, these are constrained to be consistent with the wide range of already available information about N${}^3$LO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N${}^3$LO global fit within the MSHT framework. This relies on an expansion of the Hessian procedure used in previous MSHT fits to allow for sources of theoretical uncertainties. These are included as nuisance parameters in a global fit, controlled by knowledge and intuition based prior distributions. We analyse the differences between our aN${}^3$LO PDFs and the standard NNLO PDF set, and study the impact of using aN${}^3$LO PDFs on the LHC production of a Higgs boson at this order. Finally, we provide guidelines on how these PDFs should be be used in phenomenological investigations.

arXiv comment157 pages, 51 figures, 21 tables. Updated LHAPDF Grids available which include a correction of a minor bug in the non-singlet splitting function leading to very small changes in fit quality and PDFs, but with no significant changes to any results or conclusions. Published version

References in corpus (61)

• Parton distributions for the LHC
• LHAPDF6: parton density access in the LHC precision era
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• BFKL pomeron in the next-to-leading approximation
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Energy Scale(s) and Next-to-leading BFKL Equation
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• Leptoproduction of Heavy Quarks II -- A Unified QCD Formulation of Charged and Neutral Current Processes from Fixed-target to Collider Energies
• High-Energy Factorization and Small-X Deep Inelastic Scattering Beyond Leading Order
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Fully differential VBF Higgs production at NNLO
• Resummation for QCD Hard Scattering
• Single Field Double Inflation and Primordial Black Holes
• Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
• An Ordered Analysis of Heavy Flavour Production in Deep Inelastic Scattering
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• The Structure of the Proton in the LHC Precision Era
• Leptoproduction of Heavy Quarks I-- General Formalism and Kinematics of Charged Current and Neutral Current Production Processes
• A Variable-Flavour Number Scheme for NNLO
• Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• NNLO evolution of deep-inelastic structure functions: the singlet case
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Higgs production in gluon fusion beyond NNLO
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Heavy-quark correlations in deep-inelastic electroproduction
• Dynamical scales for multi-TeV top-pair production at the LHC
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(α_s^3)
• Lepton-pair production at hadron colliders at N${}^3$LO in QCD
• On the Higgs cross section at N${}^3$LO+N${}^3$LL and its uncertainty
• On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering
• $O({\alpha }_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$
• Soft Gluon Resummation for Heavy Quark Electroproduction
• Charm-quark production in deep-inelastic neutrino scattering at NNLO in QCD
• Low moments of the four-loop splitting functions in QCD
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• Updated Higgs cross section at approximate N${}^3$LO
• The Impact of LHC Jet Data on the MMHT PDF Fit at NNLO
• Double resummation for Higgs production
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Halo-independent tests of dark matter direct detection signals: local DM density, LHC, and thermal freeze-out
• Small-$x$ phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section
• Phenomenology of NNLO jet production at the LHC and its impact on parton distributions
• On the Consistent Use of Scale Variations in PDF Fits and Predictions
• Can $\overline{\mathrm{MS}}$ parton distributions be negative?
• Positivity and renormalization of parton densities
• Pseudo-scalar Higgs Boson Production at Threshold N${}^3$LO and N${}^3$LL QCD
• Cloistered Baryogenesis
• An investigation of the ${\alpha }_S$ and heavy quark mass dependence in the MSHT20 global PDF analysis
• Correlation of Theoretical Uncertainties in PDF Fits and Theoretical Uncertainties in Predictions
• Direct Detection of Exothermic Dark Matter with Light Mediator
• Four-loop splitting functions at small $x$
• An approximate NNNLO cross section for Higgs production in gluon fusion

Cited by in corpus (49)

• 50 Years of Quantum Chromodynamics
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Neutrino Structure Functions from GeV to EeV Energies
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Parton distributions with scale uncertainties: a MonteCarlo sampling approach
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• High-energy QCD dynamics from bottom flavor fragmentation at the Hi-Lumi LHC
• Drell-Yan Transverse-Momentum Spectra at N${}^3$LL${}^{\prime }$ and Approximate N${}^4$LL with SCETlib
• Bottomoniumlike states in proton collisions: Fragmentation and resummation
• High-energy neutrino deep inelastic scattering cross sections
• Determination of the strong-coupling constant from the $Z$-boson transverse-momentum distribution
• Impact of Inclusive Electron Ion Collider Data on Collinear Parton Distributions
• Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns
• Fragmentation Functions of Charged Hadrons at Next-to-Next-to-Leading Order and Constraints on the Proton Parton Distribution Functions
• A precise measurement of the Z-boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at $\sqrt{s}$ = 8 TeV
• Combining QED and Approximate N${}^3$LO QCD Corrections in a Global PDF Fit: MSHT20qed_an3lo PDFs
• An FONLL prescription with coexisting flavor number PDFs
• A Stress Test of Global PDF Fits: Closure Testing the MSHT PDFs and a First Direct Comparison to the Neural Net Approach
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• NNLO PDFs driven by top-quark data
• Unwinding the rare $\Omega$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC
• Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop
• Electroweak, QCD and flavour physics studies with ATLAS data from Run 2 of the LHC
• A Phenomenological Analysis of LHC Neutrino Scattering at NLO Accuracy Matched to Parton Showers
• Soft-gluon corrections in $t\bar{t}W$ production
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Pseudoscalar heavy-quarkonium hadroproduction from nonrelativistic fragmentation at NLL/NLO${}^{+}$
• Robust estimates of theoretical uncertainties at fixed-order in perturbation theory
• disorder: Deep inelastic scattering at high orders
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• Deep-Inelastic Scattering at TeV Energies with LHC Muons
• Tetraquark-Jet Systems at the High-Luminosity LHC
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Resummation for $s$-channel single-top production
• N${}^3$LO soft-gluon corrections in single-particle-inclusive kinematics and $H^{+}{H}^{-}$ production
• Analysis of HERA data with a PDF parametrization inspired by quantum statistical mechanics
• Valence Quark PDFs of the Proton from Two-Current Correlations in Lattice QCD
• Next-to-leading order evolution of structure functions without PDFs
• Higgs production via vector-boson fusion at the LHC
• Determination of proton PDF uncertainties with Markov chain Monte Carlo
• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective
• QCD analysis of $x{F}_3$ structure functions in deep-inelastic scattering: Mellin transform by Gegenbauer polynomial up to N${}^3$LO approximation
• Falsifiable analog model predictions of $W$ mass in CDF II and ATLAS
• Parametrization of zero-skewness unpolarized GPDs
• Global Analyses of Generalized Parton Distributions with Diverse PDF Inputs
• 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
• Parton distribution functions and strong coupling constant: MSHT
• Higher-order soft and virtual corrections in $pp\to \gamma W$ production at the LHC