Eur. Phys. J. C (2024) 84: 1009
https://doi.org/10.1140/epjc/s10052-024-13320-5

Regular Article

A first determination of the strong coupling ${\alpha }_S$ at approximate ${\text{N}}^3$LO order in a global PDF fit

¹ Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607, Hamburg, Germany
² Department of Physics and Astronomy, University College London, WC1E 6BT, London, UK

^a thomas.cridge@desy.de

Received: 20 May 2024
Accepted: 27 August 2024
Published online: 7 October 2024

Abstract

We present the first determination of the value of the strong coupling via a simultaneous global fit of the proton parton distribution functions (PDFs) at approximate ${\text{N}}^3$LO (a${\text{N}}^3$LO) order in QCD. This makes use of the MSHT global PDF fitting framework, and in particular the recent theoretical advances t l;;mhat allow a PDF fit to now be performed at this order. The value of the strong coupling is found to be ${\alpha }_S(M_Z^2)({\mathrm{aN}}^3\mathrm{LO})=0.1170\pm 0.0016$. This is in excellent agreement with the NNLO value of ${\alpha }_S(M_Z^2)(\text{NNLO})=0.1171\pm 0.0014$, indicating that good perturbative convergence has been found. The resulting uncertainties, calculated using the MSHT dynamic tolerance procedure, are somewhat larger, but more accurate, at a${\text{N}}^3$LO, due to the missing higher order theoretical uncertainties that are included at this order, but not at NNLO. We in addition present a detailed breakdown of the individual dataset sensitivity to the value of the strong coupling, with special focus on the impact of fitting dijet rather than inclusive jet data. This choice is found to have a non-negligible impact, but with overall good consistency found, especially at a${\text{N}}^3$LO.