Uncertainties on $α_S$ in the MMHT2014 global PDF analysis and implications for SM predictions

Abstract

We investigate the uncertainty in the value of the strong coupling $α_S(M_Z^2)$ when allowing it to be a free parameter in the recent MMHT global analyses of deep-inelastic and related hard scattering data that was undertaken to determine the parton distribution functions (PDFs) of the proton. The analysis uses the standard framework of leading twist fixed--order collinear factorisation in the ${\overline {\rm MS}}$ scheme. We study the constraints on the value of $α_S(M_Z^2)$ coming from the individual data sets by repeating the NNLO and NLO global analyses at various fixed values of $α_S(M_Z^2)$ about its optimum values, spanning the range $α_S(M_Z^2)=0.108$ to $0.128$ in units of $0.001$, and making all PDFs sets available. The inclusion of the measurements of the cross section for inclusive $t\bar{t}$ production in the global fit allows us to explore the correlation between the values taken for the mass $m_t$ of the top quark and $α_S(M_Z^2)$. We find that the best fit values are $α_S(M_Z^2)=0.1201\pm0.0015$ and $0.1172\pm 0.0013$ at NLO and NNLO respectively, with the central values changing to $α_S(M_Z^2)=0.1195$ and $0.1178$ when the world average of $α_S(M_Z^2)$ is used as a data point. We investigate the interplay between the uncertainties on $α_S(M_Z^2)$ and the uncertainties on the PDFs. In particular we calculate the cross sections for key processes at the LHC and show how the uncertainties coming from the standard MMHT2014 PDFs and from $α_S(M_Z^2)$ can be provided independently and can be combined.