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We investigate the MSHT20 global PDF sets, demonstrating the effects ofvarying the strong coupling $\alpha_S(M_Z^2)$ and the masses of the charm andbottom quarks. We determine the preferred value, and accompanyinguncertainties, when we allow $\alpha_S(M_Z^2)$ to be a free parameter in theMSHT20 global analyses of deep-inelastic and related hard scattering data, atboth 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 byrepeating 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 $0.130$ inunits of $0.001$. We make all resulting PDFs sets available. We find that thebest 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 thevariations in $\alpha_S(M_Z^2)$ and the uncertainties on the PDFs, andillustrate 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 $m_b$ tovary away from their default values and make PDF sets available in steps of$\Delta m_c =0.05~{\rm GeV}$ and $\Delta m_b =0.25~{\rm GeV}$, using the polemass 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 thecomparison to data, particularly the HERA data on charm and bottom crosssections and note that our default values are very largely compatible with bestfits to data. We provide PDF sets with 3 and 4 active quark flavours, as wellas the standard value of 5 flavours.

An investigation of the $\alpha_S$ and heavy quark mass dependence in the MSHT20 global PDF analysis