Papers › Approximate N³LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN³LO PDFs
Approximate N³LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN³LO PDFs
J. McGowan, T. Cridge, L. A. Harland-Lang, R. S. Thorne
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We present the first global analysis of parton distribution functions (PDFs) at approximate N³LO in the strong coupling constant αₛ, 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 (N³LO) in αₛ can provide consistent, justifiable and explainable approximate N³LO (aN³LO) PDFs. This includes estimates for uncertainties due the the currently unknown N³LO 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 N³LO. Crucially, these are constrained to be consistent with the wide range of already available information about N³LO to match the complete result at this order as accurately as possible. Using this approach we perform a fully consistent approximate N³LO 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 aN³LO PDFs and the standard NNLO PDF set, and study the impact of using aN³LO 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.
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