An investigation of the $$\alpha _S$$ α S and heavy quark mass dependence in the MSHT20 global PDF analysis

We investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $$\alpha _S(M_Z^2)$$ and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $$\alpha _S(M_Z^2)$$ to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $$\alpha _S(M_Z^2)$$ which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $$\alpha _S(M_Z^2)$$ , spanning the range $$\alpha _S(M_Z^2)=0.108$$ to 0.130 in units of 0.001. We make all resulting PDFs sets available. We find that the best fit values are $$\alpha _S(M_Z^2)=0.1203\pm 0.0015$$ and $$0.1174\pm 0.0013$$ at NLO and NNLO respectively. We investigate the relationship between the variations in $$\alpha _S(M_Z^2)$$ and the uncertainties on the PDFs, and illustrate this by calculating the cross sections for key processes at the LHC. We also perform fits where we allow the heavy quark masses $$m_c$$ and $$m_b$$ to vary away from their default values and make PDF sets available in steps of $$\Delta m_c =0.05~\mathrm GeV$$ and $$\Delta m_b =0.25~\mathrm GeV$$ , using the pole mass definition of the quark masses. As for varying $$\alpha _S(M_Z^2)$$ values, we present the variation in the PDFs and in the predictions. We examine the comparison to data, particularly the HERA data on charm and bottom cross sections and note that our default values are very largely compatible with best fits to data. We provide PDF sets with 3 and 4 active quark flavours, as well as the standard value of 5 flavours.