An investigation of the αS 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 αS(M2Z) and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow αS(M2Z) 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 αS(M2Z) which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of αS(M2Z), spanning the range αS(M2Z)=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 αS(M2Z)=0.1203±0.0015 and 0.1174±0.0013 at NLO and NNLO respectively. We investigate the relationship between the variations in αS(M2Z) 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 mc and mb to vary away from their default values and make PDF sets available in steps of Δmc=0.05 GeV and Δmb=0.25 GeV, using the pole mass definition of the quark masses. As for varying αS(M2Z) 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

On the consistent use of scale variations in PDF fits and predictions

We present an investigation of the theoretical uncertainties in parton distribution functions (PDFs) due to missing higher-order corrections in the perturbative predictions used in the fit, and their relationship to the uncertainties in subsequent predictions made using the PDFs. We consider in particular the standard approach of factorization and renormalization scale variation, and derive general results for the consistent application of these at the PDF fit stage. To do this, we use the fact that a PDF fit may be recast in a physical basis, where the PDFs themselves are bypassed entirely, and one instead relates measured observables to predicted ones. In the case of factorization scale variation we find that in various situations there is a high degree of effective correlation between the variation in the fit and in predicted observables. In particular, including such a variation in both cases can lead to an exaggerated theoretical uncertainty. More generally, a careful treatment of this correlation appears mandatory, at least within the standard scale variation paradigm. For the renormalization scale, the situation is less straightforward, but again we highlight the potential for correlations between related processes in the fit and predictions to enter at the same level as between processes in the fit or prediction alone

Updates of the MMHT2014 PDFs

We briefly discuss some of the developments since the publication of the MMHT14 parton distributions. In particular we explore the impact of recent LHC data for W±, Z and tt¯production, and perform a preliminary new analysis including these data. In this re-fit (which we tentatively call ‘MMHT16’) there are few changes of significance in the central values of the PDFs, but some data reduce the uncertainties, mainly in the strange and valence quark distributions. We find that an extended d¯− u¯ parametrization only leads to minor changes, with the difference going to zero as x → 0. We comment on the determination of the photon PDF

Updates of the MMHT2014 PDFs

We briefly discuss some of the developments since the publication of the MMHT14 parton distributions. In particular we explore the impact of recent LHC data for W±, Z and tt¯production, and perform a preliminary new analysis including these data. In this re-fit (which we tentatively call ‘MMHT16’) there are few changes of significance in the central values of the PDFs, but some data reduce the uncertainties, mainly in the strange and valence quark distributions. We find that an extended d¯− u¯ parametrization only leads to minor changes, with the difference going to zero as x → 0. We comment on the determination of the photon PDF

Charm in Deep-Inelastic Scattering

We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions $F^c_2$, $F^c_L$ and $F^c_3$ to NNLO