Search

We present the first determination of the value of the strong coupling via a simultaneous global fit of the proton parton distribution functions (PDFs) at approximate N 3 LO (a N 3 LO) order in QCD. This makes use of the MSHT global PDF fitting framework, and in particular the recent theoretical advances t l;;mhat allow a PDF fit to now be performed at this order. The value of the strong coupling is found to be α S ( M Z 2 ) ( aN 3 LO ) = 0.1170 ± 0.0016 . This is in excellent agreement with the NNLO value of α S ( M Z 2 ) ( NNLO ) = 0.1171 ± 0.0014 , indicating that good perturbative convergence has been found. The resulting uncertainties, calculated using the MSHT dynamic tolerance procedure, are somewhat larger, but more accurate, at a N 3 LO, due to the missing higher order theoretical uncertainties that are included at this order, but not at NNLO. We in addition present a detailed breakdown of the individual dataset sensitivity to the value of the strong coupling, with special focus on the impact of fitting dijet rather than inclusive jet data. This choice is found to have a non-negligible impact, but with overall good consistency found, especially at a N 3 LO., (© The Author(s) 2024.)

We investigate the impact of the high precision ATLAS and CMS 7 TeV measurements of inclusive jet production on the MMHT global PDF analysis at next-to-next-to-leading order (NNLO). This is made possible by the recent completion of the long-term project to calculate the NNLO corrections to the hard cross section. We find that a good description of the ATLAS data is not possible with the default treatment of experimental systematic errors, and propose a simplified solution that retains the dominant physical information of the data. We then investigate the fit quality and the impact on the gluon PDF central value and uncertainty when the ATLAS and CMS data are included in a MMHT fit. We consider both common choices for the factorization and renormalization scale, namely the inclusive jet transverse momentum, p ⊥ , and the leading jet p ⊥ , as well as the different jet radii for which the ATLAS and CMS data are made available. We find that the impact of these data on the gluon is relatively insensitive to these inputs, in particular the scale choice, while the inclusion of NNLO corrections tends to improve the data description somewhat and has a qualitatively similar though not identical impact on the gluon in comparison to NLO.

We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and the uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in [Formula: see text] and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of [Formula: see text]. This can be improved by phenomenologically motived corrections to [Formula: see text] which parametrically are largely in the form of higher-twist type contributions.

We investigate the variation in the MMHT2014 PDFs when we allow the heavy-quark masses [Formula: see text] and [Formula: see text] to vary away from their default values. We make PDF sets available in steps of [Formula: see text] and [Formula: see text], and present the variation in the PDFs and in the predictions. We examine the comparison to the HERA data on charm and beauty structure functions and note that in each case the heavy-quark data, and the inclusive data, have a slight preference for lower masses than our default values. We provide PDF sets with three and four active quark flavours, as well as the standard value of five flavours. We use the pole mass definition of the quark masses, as in the default MMHT2014 analysis, but briefly comment on the [Formula: see text] definition.

We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the 'MSTW2008' parton sets, but they are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the 'MSTW2008' parton sets. In most cases the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the [Formula: see text] valence quark difference at small [Formula: see text] due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of certain LHC data and a better treatment of the [Formula: see text] branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary with the present analysis.

We investigate the uncertainty in the strong coupling [Formula: see text] 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 [Formula: see text] scheme. We study the constraints on [Formula: see text] coming from individual data sets by repeating the NNLO and NLO fits spanning the range 0.108 to 0.128 in units of 0.001, making all PDFs sets available. The inclusion of the cross section for inclusive [Formula: see text] production allows us to explore the correlation between the mass [Formula: see text] of the top quark and [Formula: see text]. We find that the best-fit values are [Formula: see text] and [Formula: see text] at NLO and NNLO, respectively, with the central values changing to [Formula: see text] and 0.1178 when the world average of [Formula: see text] is used as a data point. We investigate the interplay between the uncertainties on [Formula: see text] and on the PDFs. In particular we calculate the cross sections for key processes at the LHC and show how the uncertainties from the PDFs and from [Formula: see text] can be provided independently and be combined.

I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small [Formula: see text] values, the gluon distribution becoming smaller at high values of [Formula: see text] and larger at small [Formula: see text], the preferred value of the coupling constant [Formula: see text] falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on [Formula: see text] for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and [Formula: see text] than the scheme change, except for quarks at very high [Formula: see text]. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for [Formula: see text] at high [Formula: see text], and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form [Formula: see text] relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.

We consider the effect on LHC jet cross sections on partons distribution functions (PDFs), in particular the MSTW2008 set of PDFs. We first compare the published inclusive jet data to the predictions using MSTW2008, finding a very good description. We also use the parton distribution reweighting procedure to estimate the impact of these new data on the PDFs, finding that the combined ATLAS 2.76 and 7 TeV data, and CMS 7 TeV data have some significant impact. We then also investigate the impact of ATLAS, CMS and DØ dijet data using the same techniques. In this case we investigate the effect of using different scale choices for the NLO cross section calculation. We find that the dijet data is generally not completely compatible with the corresponding inclusive jet data, often tending to pull PDFs, particularly the gluon distribution, away from the default values. However, the effect depends on the dijet dataset used as well as the scale choice. We also note that conclusions may be affected by limiting the pull on the data luminosity chosen by the best fit, which is sometimes a number of standard deviations. Finally we include the inclusive jet data in a new PDF fit explicitly. This enables us to check the consistency of the exact result with that obtained from the reweighting procedure. There is generally good, but not full quantitative agreement. Hence, the conclusion remains that MSTW2008 PDFs already fit the published jet data well, but the central values and uncertainties are altered and improved, respectively, to a significant, but not dramatic extent by inclusion of these data.