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.

157 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 (20)

• Parton distributions for the LHC
• LHAPDF6: parton density access in the LHC precision era
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• 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
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• 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
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Lepton-pair production at hadron colliders at N${}^3$LO 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
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Phenomenology of NNLO jet production at the LHC and its impact on parton distributions
• Can $\overline{\mathrm{MS}}$ parton distributions be negative?
• Positivity and renormalization of parton densities
• 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

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