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

We investigate the uncertainty in the value of the strong coupling $\alpha_S(M_Z^2)$ 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 $\alpha_S(M_Z^2)$ coming from the individual data sets by repeating the NNLO and NLO global analyses at various fixed values of $\alpha_S(M_Z^2)$ about its optimum values, spanning the range $\alpha_S(M_Z^2)=0.108$ 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 $\alpha_S(M_Z^2)$. We find that the best fit values are $\alpha_S(M_Z^2)=0.1201\pm0.0015$ and $0.1172\pm 0.0013$ at NLO and NNLO respectively, with the central values changing to $\alpha_S(M_Z^2)=0.1195$ and $0.1178$ when the world average of $\alpha_S(M_Z^2)$ is used as a data point. We investigate the interplay between the uncertainties on $\alpha_S(M_Z^2)$ 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 $\alpha_S(M_Z^2)$ can be provided independently and can be combined.