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This review is devoted to the study of charm production in ep and pp collisions. The total set of measurements obtained by the two collaborations H1 and ZEUS from HERA and their combination is outlined, as well as complementary data obtained by the LHCb Collaboration at the LHC. After fitting the parton distribution functions the charm-production cross sections are predicted within perturbative QCD at next-to-leading order using the fixed-flavour-number scheme. Agreement with the data is found. The combined HERA charm data are sensitive to the c -quark mass and enabled its accurate determination. The predictions crucially depend upon the knowledge of the gluon distribution function. It is shown that the shape of the gluon distribution based on the HERA data is considerably improved by adding the measurements from LHCb and applicable down to values x of about 10 - 6 , where x is the proton momentum fraction carried by a parton.

We study the impact of state-of-the-art top-quark data collected at the large hadron collider on parton distribution functions (PDFs). Following the ABMP methodology, the fit extracts simultaneously proton PDFs, the strong coupling α s ( M Z ) and heavy-quark masses at next-to-next-to-leading order (NNLO) accuracy in QCD. It includes recent high-statistics data on absolute total inclusive cross sections for    t t ¯ + X , the sum of ( t + X ) and ( t ¯ + X ) hadroproduction, and normalized inclusive data double-differential in the invariant mass and rapidity of the t t ¯ pair at S = 13  TeV. The gluon PDF at large x and the top-quark mass value derived from these data are well compatible with the previous ABMP16 results, but with significantly smaller uncertainties, reduced by up to a factor of two. At NNLO in QCD we obtain for the strong coupling the value α s ( n f = 5 ) ( M Z ) = 0.1150 ± 0.0009 and for the top-quark mass in the MS ¯ -scheme m t ( m t ) = 160.6 ± 0.6  GeV, corresponding to m t pole = 170.2 ± 0.7  GeV in the on-shell scheme. The new fit, dubbed ABMPtt, is publicly released in grids in LHAPDF format.

We determine the strong coupling from high-energy data for the Drell–Yan process and top-quark hadro-production collected at the Large Hadron Collider and the Tevatron combined with the world data on deep-inelastic scattering (DIS) and fixed-target Drell–Yan data. The theory description uses results at next-to-next-to-leading order in perturbative QCD in the MS ¯ -scheme together with leading order QED evolution. The DIS data are subject to stringent kinematic cuts to suppress the contribution of power corrections. We apply a cut on the hadronic invariant mass squared W 2 ≥ 12.5 GeV 2 together with a series of cuts on momentum transfer squared Q 2 . Discarding higher-twist terms we find that the value of strong coupling α s ( m Z ) preferred by the data stabilizes at large enough cuts on Q 2 , when low- Q 2 DIS data sensitive to power corrections are effectively removed. In particular, we extract the value of α s ( m Z , N f = 5 ) = 0.1152 ± 0.0008 for N f = 5 light flavors with the cut Q 2 > 10 GeV 2 . In the absence of higher-twist terms less tight cuts on Q 2 show a clear deterioration of the fit and lead to rising values of the strong coupling, shifted upwards by about two standard deviations.

A bstract The impact of measurements of heavy-flavour production in deep inelastic ep scattering and in pp collisions on parton distribution functions is studied in a QCD analysis at next-to-leading order. Recent combined results of inclusive and heavy-flavour produc- tion cross sections in deep inelastic scattering at HERA are investigated together with heavy-flavour production measurements at the LHC. Differential cross sections of charm- and beauty-hadron production measured by the LHCb collaboration at the centre-of-mass energies of 5, 7 and 13 TeV as well as the recent measurements of the ALICE experiment at the centre-of-mass energies of 5 and 7 TeV are explored. These data impose additional constraints on the gluon and the sea-quark distributions at low partonic fractions x of the proton momentum, down to x ≈ 10 − 6 . The impact of the resulting parton distribution function in the predictions for the prompt atmospheric-neutrino fluxes is studied.

We review the present status of the determination of parton distribution functions (PDFs) in the light of the precision requirements for the LHC in Run 2 and other future hadron colliders. We provide brief reviews of all currently available PDF sets and use them to compute cross sections for a number of benchmark processes, including Higgs boson production in gluon–gluon fusion at the LHC. We show that the differences in the predictions obtained with the various PDFs are due to particular theory assumptions made in the fits of those PDFs. We discuss PDF uncertainties in the kinematic region covered by the LHC and on averaging procedures for PDFs, such as advocated by the PDF4LHC15 sets, and provide recommendations for the usage of PDF sets for theory predictions at the LHC.

A bstract Effects on atmospheric prompt neutrino fluxes of present uncertainties affecting the nucleon composition are studied by using the PROSA fit to parton distribution functions (PDFs). The PROSA fit extends the precision of the PDFs to low x , which is the kinematic region of relevance for high-energy neutrino production, by taking into account LHCb data on charm and bottom hadroproduction collected at the center-of-mass energy of s = 7 TeV. In the range of neutrino energies explored by present Very Large Volume Neutrino Telescopes, it is found that PDF uncertainties are far smaller with respect to those due to renormalization and factorization scale variation and to assumptions on the cosmic ray composition, which at present dominate and limit our knowledge of prompt neutrino fluxes. A discussion is presented on how these uncertainties affect the expected number of atmospheric prompt neutrino events in the analysis of high-energy events characterized by interaction vertices fully contained within the instrumented volume of the detector, performed by the IceCube collaboration.

A bstract We extract the top-quark mass value in the on-shell renormalization scheme from the comparison of theoretical predictions for pp → t t ¯ + X at next-to-next-to-leading order (NNLO) QCD accuracy with experimental data collected by the ATLAS and CMS collaborations for absolute total, normalized single-differential and double-differential cross-sections during Run 1, Run 2 and the ongoing Run 3 at the Large Hadron Collider (LHC). For the theory computations of heavy-quark pair-production we use the MATRIX framework, interfaced to PineAPPL for the generation of grids of theory predictions, which can be efficiently used a-posteriori during the fit, performed within xFitter. We take several state-of-the-art parton distribution functions (PDFs) as input for the fit and evaluate their associated uncertainties, as well as the uncertainties arising from renormalization and factorization scale variation. Fit uncertainties related to the datasets are also part of the extracted uncertainty of the top-quark mass and turn out to be of similar size as the combined scale and PDF uncertainty. Fit results from different PDF sets agree among each other within 1 σ uncertainty, whereas some datasets related to t t ¯ decay in different channels (dileptonic vs. semileptonic) point towards top-quark mass values in slight tension among each other, although still compatible within 2 . 5 σ accuracy. Our results are compatible with the PDG 2022 top-quark pole-mass value. Our work opens the road towards more complex simultaneous NNLO fits of PDFs, the strong coupling α s ( M Z ) and the top-quark mass, using the currently most precise experimental data on t t ¯ + X total and multi-differential cross sections from the LHC.

A bstract We present predictions for heavy-quark production at the Large Hadron Collider making use of the MS ¯ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, MCFM and xFitter, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential t t ¯ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low x values, from available LHC data on heavy-flavor hadro-production.

Measurements of open charm and beauty production cross sections in deep inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections are obtained in the kinematic range of negative four-momentum transfer squared of the photon 2.5GeV2≤Q2≤2000GeV2 and Bjorken scaling variable 3·10-5≤xBj≤5·10-2. The combination method accounts for the correlations of the statistical and systematic uncertainties among the different datasets. Perturbative QCD calculations are compared to the combined data. A next-to-leading order QCD analysis is performed using these data together with the combined inclusive deep inelastic scattering cross sections from HERA. The running charm- and beauty-quark masses are determined as mc(mc)=1.290-0.041+0.046(exp/fit)-0.014+0.062(model)-0.031+0.003(parameterisation) GeV and mb(mb)=4.049-0.109+0.104(exp/fit)-0.032+0.090(model)-0.031+0.001(parameterisation)GeV.

The impact of recent measurements of heavy-flavour production in deep inelastic ep scattering and in pp collisions on parton distribution functions is studied in a QCD analysis in the fixed-flavour number scheme at next-to-leading order. Differential cross sections of charm- and beauty-hadron production measured by LHCb are used together with inclusive and heavy-flavour production cross sections in deep inelastic scattering at HERA. The heavy-flavour data of the LHCb experiment impose additional constraints on the gluon and the sea-quark distributions at low partonic fractions x of the proton momentum, down to x ∼ 5 × 10 - 6 . This kinematic range is currently not covered by other experimental data in perturbative QCD fits.