Eur. Phys. J. C (2025) 85: 1001
https://doi.org/10.1140/epjc/s10052-025-14676-y

Regular Article - Theoretical Physics

A determination of ${\alpha }_s(m_Z)$ at ${\text{aN}}^3{\text{LO}}_{\text{QCD}}\otimes {\text{NLO}}_{\text{QED}}$ accuracy from a global PDF analysis

¹ The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd, EH9 3JZ, Edinburgh, Scotland
² Tif Lab, Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133, Milan, Italy
³ Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
⁴ Department of Physics, University of Jyvaskyla, P.O. Box 35, 40014, Jyvaskyla, Finland
⁵ Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, 00014, Helsinki, Finland
⁶ Dipartimento di Fisica and INFN, Sezione di Torino, Università degli Studi di Torino, Via Pietro Giuria 1, 10125, Turin, Italy
⁷ Department of Physics and Astronomy, Vrije Universiteit, 1081 HV, Amsterdam, The Netherlands
⁸ Nikhef Theory Group, Science Park, 105, 1098 XG, Amsterdam, The Netherlands

Received: 4 July 2025
Accepted: 26 August 2025
Published online: 16 September 2025

Abstract

We present a determination of the strong coupling ${\alpha }_s(m_Z)$ from a global dataset including both fixed-target and collider data from deep-inelastic scattering and a variety of hadronic processes, with a simultaneous determination of parton distribution functions (PDFs) based on the NNPDF4.0 methodology. This determination is performed at NNLO and approximate ${\text{N}}^3$LO (${\text{aN}}^3$LO) perturbative QCD accuracy, including QED corrections and a photon PDF up to NLO accuracy. We extract ${\alpha }_s$ using two independent methodologies, both of which take into account the cross-correlation between ${\alpha }_s$ and the PDFs. The two methodologies are validated by closure tests that allow us to detect and remove or correct for several sources of bias, and lead to mutually consistent results. We account for all correlated experimental uncertainties, as well as correlated theoretical uncertainties related to missing higher order perturbative corrections (MHOUs). We study the perturbative convergence of our results and the impact of QED corrections. We assess individual sources of uncertainty, specifically MHOUs and the value of the top quark mass. We provide a detailed appraisal of methodological choices, including the choice of input dataset, the form of solution of evolution equation, the treatment of the experimental covariance matrix, and the details of Monte Carlo data generation. We find ${\alpha }_s(m_Z)=0.{1194}_{-0.0014}^{+0.0007}$ at ${\text{aN}}^3$${\text{LO}}_{\text{QCD}}\otimes {\text{NLO}}_{\text{QED}}$ accuracy, consistent with the latest PDG average and with recent lattice results.