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We review progress in the global QCD analysis by the CTEQ-TEA group since the publication of CT18 parton distribution functions (PDFs) in the proton. Specifically, we discuss comparisons of CT18 NNLO predictions with the LHC 13 TeV measurements as well as with the FNAL SeaQuest and BNL STAR data on lepton pair production. The specialized CT18X PDFs approximating saturation effects are compared with the CT18sx PDFs obtained using NLL/NLO small-$x$ resummation. Short summaries are presented for the special CT18 parton distributions with fitted charm and with lattice QCD inputs. A recent comparative analysis of the impact of deuteron nuclear effects on the parton distributions by the CTEQ-JLab and CTEQ-TEA groups is summarized.

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Experimental measurements in deep-inelastic scattering and lepton-pair production on deuterium targets play an important role in the flavor separation of u and d (anti)quarks in global QCD analyses of the parton distribution functions (PDFs) of the nucleon. We investigate the impact of theoretical corrections accounting for the light-nuclear structure of the deuteron upon the fitted u , d -quark, gluon, and other PDFs in the CJ15 and CT18 families of next-to-leading order CTEQ global analyses. The investigation is done using the $$L_2$$ L 2 sensitivity statistical method, which provides a common metric to quantify the strength of experimental constraints on various PDFs and ratios of PDFs in the two distinct fitting frameworks. Using the $$L_2$$ L 2 sensitivity and other approaches, we examine the compatibility of deuteron data sets with other fitted experiments under varied implementations of the deuteron corrections. We find that freely-fitted deuteron corrections modify the PDF uncertainty at large momentum fractions and will be relevant for future PDFs affecting electroweak precision measurements.

We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from global analyses of the available hard scattering data. The PDFs are made available at NNLO, NLO, and LO, and supersede the MMHT14 sets. They are obtained using the same basic framework, but the parameterisation is now adapted and extended, and there are 32 pairs of eigenvector PDFs. We also include a large number of new data sets: from the final HERA combined data on total and heavy flavour structure functions, to final Tevatron data, and in particular a significant number of new LHC 7 and 8 TeV data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit, and NLO EW corrections where relevant. We find that these updates have an important impact on the PDFs, and for the first time the NNLO fit is strongly favoured over the NLO, reflecting the wider range and in particular increased precision of data included in the fit. There are some changes to central values and a significant reduction in the uncertainties of the PDFs in many, though not all, cases. Nonetheless, the PDFs and the resulting predictions are generally within one standard deviation of the MMHT14 results. The major changes are the $$u-d$$ u - d valence quark difference at small x , due to the improved parameterisation and new precise data, the $${\bar{d}}, {\bar{u}}$$ d ¯ , u ¯ difference at small x , due to a much improved parameterisation, and the strange quark PDF due to the effect of LHC W , Z data and inclusion of new NNLO corrections for dimuon production in neutrino DIS. We discuss the phenomenological impact of our results, and in general find reduced uncertainties in predictions for processes such as Higgs, top quark pair and W , Z production at post LHC Run-II energies.

We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions x. Analytic functional forms for PDFs cannot be uniquely determined solely based on discrete experimental measurements because of a mathematical property of mimicry of PDF parametrizations that we prove using a representation based on Bézier curves. Predictions of nonperturbative QCD approaches for the x dependence of PDFs instead should be cast in a form that enables decisive comparisons against experimental measurements. Predictions for effective power laws of (1−x) dependence of PDFs may play this role. Expectations for PDFs in a proton based on quark counting rules are compared against the effective power laws of (1−x) dependence satisfied by CT18 next-to-next-to-leading-order parton distributions. We comment on implications for studies of PDFs in a pion, in particular on the comparison of nonperturbative approaches with phenomenological PDFs.

The fundamental building blocks of the proton—quarks and gluons—have been known for decades. However, we still have an incomplete theoretical and experimental understanding of how these particles and their dynamics give rise to the quantum bound state of the proton and its physical properties, such as its spin1. The two up quarks and the single down quark that comprise the proton in the simplest picture account only for a few per cent of the proton mass, the bulk of which is in the form of quark kinetic and potential energy and gluon energy from the strong force2. An essential feature of this force, as described by quantum chromodynamics, is its ability to create matter–antimatter quark pairs inside the proton that exist only for a very short time. Their fleeting existence makes the antimatter quarks within protons difficult to study, but their existence is discernible in reactions in which a matter–antimatter quark pair annihilates. In this picture of quark–antiquark creation by the strong force, the probability distributions as a function of momentum for the presence of up and down antimatter quarks should be nearly identical, given that their masses are very similar and small compared to the mass of the proton3. Here we provide evidence from muon pair production measurements that these distributions are considerably different, with more abundant down antimatter quarks than up antimatter quarks over a wide range of momenta. These results are expected to revive interest in several proposed mechanisms for the origin of this antimatter asymmetry in the proton that had been disfavoured by previous results4, and point to future measurements that can distinguish between these mechanisms. Quark–antiquark annihilation measurements provide a precise determination of the ratio of down and up antiquarks within protons as a function of momentum, which confirms the asymmetry between the abundance of down and up antiquarks.

We present the new parton distribution functions (PDFs) from the CTEQ-TEA collaboration, obtained using a wide variety of high-precision Large Hadron Collider (LHC) data, in addition to the combined HERA I+II deep-inelastic scattering dataset, along with the datasets present in the CT14 global QCD analysis. New LHC measurements in single-inclusive jet production with the full rapidity coverage, as well as production of Drell-Yan pairs, top-quark pairs, and high-pT Z bosons, are included to achieve the greatest sensitivity to the PDFs. The parton distributions are determined at next-to-leading order and next-to-next-to-leading order, with each of these PDFs accompanied by error sets determined using the Hessian method. Fast PDF survey techniques, based on the Hessian representation and the Lagrange multiplier method, are used to quantify the preference of each data set to quantities such as αs(mZ), and the gluon and strange quark distributions. We designate the main resulting PDF set as CT18. The ATLAS 7 TeV precision W/Z data are not included in CT18, due to their tension with other datasets in the global fit. Alternate PDF sets are generated including the ATLAS precision 7 TeV W/Z data (CT18A), a new scale choice for low-x DIS data (CT18X), or all of the above with a slightly higher choice for the charm mass (CT18Z). Theoretical calculations of standard candle cross sections at the LHC (such as the gg fusion Higgs boson cross section) are presented.

We perform the first simultaneous extraction of unpolarized parton distributions and fragmentation functions from a Monte Carlo analysis of inclusive and semi-inclusive deep-inelastic scattering, Drell-Yan lepton-pair production, and single-inclusive e+e− annihilation data. We use data resampling techniques to thoroughly explore the Bayesian posterior distribution of the extracted functions, and use k-means clustering on the parameter samples to identify the configurations that give the best description across all reactions. Inclusion of the semi-inclusive data reveals a strong suppression of the strange quark distribution at parton momentum fractions x≳0.01, in contrast with the ATLAS observation of enhanced strangeness in W± and Z production at the LHC. Our study reveals significant correlations between the strange quark density and the strange → kaon fragmentation function needed to simultaneously describe semi-inclusive K± production data from COMPASS and inclusive K± spectra in e+e− annihilation from ALEPH and SLD, as well as between the strange and light antiquark densities in the proton.

A bstract
Without proper control of numerical and methodological errors in theoretical predictions at the per mille level it is not possible to study the effect of input parameters in current hadron-collider measurements at the required precision. We present the new version of the parton-level code MCFM-9.0 that achieves this requirement through its highly-parallelized nature, significant performance improvements and new features. An automatic differential jettiness slicing cutoff extrapolation is introduced to assess the cutoff dependence of all results, thus ensuring their reliability and potentially improving fixed- cutoff results by an order of magnitude. The efficient differential study of PDF uncertainties and PDF set differences at NNLO, for multiple PDF sets simultaneously, is achieved by exploiting correlations. We use these improvements to study uncertainties and PDF sensitivity at NNLO, using 371 PDF set members. The work described here permits NNLO studies that were previously prohibitively expensive, and lays the groundwork necessary for a future implementation of NNLO calculations with a jet at Born level in MCFM.

Building upon the PDFSense framework developed in Wang et al. [Phys. Rev. D 98, 094030 (2018)], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions, such as ⟨x⟩u+−d+ and ⟨x⟩g, as well as x-dependent quark quasidistributions—in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleon’s collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.

Determinations of the proton’s collinear parton distribution functions (PDFs) are emerging with growing precision due to increased experimental activity at facilities like the Large Hadron Collider. While this copious information is valuable, the speed at which it is released makes it difficult to quickly assess its impact on the PDFs, short of performing computationally expensive global fits. As an alternative, we explore new methods for quantifying the potential impact of experimental data on the extraction of proton PDFs. Our approach relies crucially on the Hessian correlation between theory-data residuals and the PDFs themselves, as well as on a newly defined quantity—the sensitivity—which represents an extension of the correlation and reflects both PDF-driven and experimental uncertainties. This approach is realized in a new, publicly available analysis package PDFSense, which operates with these statistical measures to identify particularly sensitive experiments, weigh their relative or potential impact on PDFs, and visualize their detailed distributions in a space of the parton momentum fraction x and factorization scale μ. This tool offers a new means of understanding the influence of individual measurements in existing fits as well as a predictive device for directing future fits toward the highest impact data and assumptions. Along the way, many new physics insights can be gained or reinforced. As one of many examples, PDFSense is employed to rank the projected impact of new LHC measurements in jet, vector boson, and tt¯ production and leads us to the conclusion that inclusive jet production at the LHC has a potential for playing an indispensable role in future PDF fits. These conclusions are independently verified by preliminarily fitting this experimental information and investigating the constraints they supply using the Lagrange multiplier technique.

We discuss how to apply the Hessian method (i) to predict the impact of a new data set (or sets) on the parton distribution functions (PDFs) and their errors, by producing an updated best-fit PDF and error PDF sets, such as the CTEQ-TEA PDFs; (ii) to predict directly the effect of a new data set on the PDF errors of any other set of observables, without the need to recalculate using the new error PDFs; and (iii) to transform the original set into a reduced set of error PDFs which is optimized for a specific set of observables to reproduce the PDF-induced uncertainties to any specified precision. We present a software package, ePump (Error PDF Updating Method Package), that can be used to update or optimize a set of PDFs, including the best-fit PDF set and Hessian eigenvector pairs of PDF sets (i.e., error PDFs), and to update any other set of observables. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the Large Hadron Collider. Special care is given to discuss the assumptions made and the limitations of this theoretical framework compared to a treatment by the full global-analysis program.

Fits to the final combined HERA deep-inelastic scattering cross-section data within the conventional DGLAP framework of QCD have shown some tension at low x and low \(Q^2\). A resolution of this tension incorporating \(\ln (1/x)\)-resummation terms into the HERAPDF fits is investigated using the xFitter program. The kinematic region where this resummation is important is delineated. Such high-energy resummation not only gives a better description of the data, particularly of the longitudinal structure function \(F_L\), it also results in a gluon PDF which is steeply rising at low x for low scales, \(Q^2 \simeq 2.5\,\hbox {GeV}^2\), contrary to the fixed-order NLO and NNLO gluon PDF.

We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep-inelastic structure functions are computed consistently at
NLO+NLL
x
or
NNLO+NLL
x
, while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the recent NNPDF3.1 analysis. We demonstrate that the inclusion of small-x resummation leads to a quantitative improvement in the perturbative description of the HERA inclusive and charm-production reduced cross-sections in the small x region. The impact of the resummation in our fits is greater at NNLO than at NLO, because fixed-order calculations have a perturbative instability at small x due to large logarithms that can be cured by resummation. We explore the phenomenological implications of PDF sets with small-x resummation for the longitudinal structure function
F
L
at HERA, for parton luminosities and LHC benchmark cross-sections, for ultra-high-energy neutrino-nucleus cross-sections, and for future high-energy lepton-proton colliders such as the LHeC.

In global fits of parton distribution functions (PDFs) a large fraction of data points, mostly from the HERA collider, lies in a region of $x$ and $Q^2$ that is sensitive to small-$x$ logarithmic enhancements. Thus, the proper theoretical description of these data requires the inclusion of small-$x$ resummation. In this work we provide all the necessary ingredients to perform a PDF fit to deep-inelastic scattering (DIS) data which includes small-$x$ resummation in the evolution of PDFs and in the computation of DIS structure functions. To this purpose, not only we include the resummation of DIS massless structure functions, but we also consider the production of a massive final state (e.g. a charm quark), and the consistent resummation of mass collinear logarithms through the implementation of a variable flavour number scheme at small $x$. As a result, we perform the small-$x$ resummation of the matching conditions in PDF evolution at heavy flavour thresholds. The resummed results are accurate at next-to-leading logarithmic (NLL) accuracy and matched, for the first time, to next-to-next-to-leading order (NNLO). Furthermore, we improve on our previous work by considering a novel all-order treatment of running coupling contributions. These results, which are implemented in a new release of HELL, version 2.0, will allow to fit PDFs from DIS data at the highest possible theoretical accuracy, NNLO+NLL, thus providing an important step forward towards precision determination of PDFs and consequently precision phenomenology at the LHC and beyond.

In the context of the CTEQ-TEA global QCD analysis, we study the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon and its potential impact on LHC scattering processes. We address theoretical issues arising in studies of the nonperturbative charm, its dynamical origin in the context of the QCD factorization theorem, and the need to distinguish the genuine nonperturbative (power-suppressed) component from various comparable radiative contributions in global fits to QCD data. Under the assumption that factorization exists for a fitted charm PDF, we determine the range of its magnitude allowed in the CT14 global QCD analysis at the next-to-next-to leading order in the QCD coupling strength, including the latest experimental data from HERA and the Large Hadron Collider. Models for the charm PDF in the nucleon are examined as a function of the charm pole mass and other parameters. The prospects for testing the nonperturbative charm models in the associated production of a Z boson and a charm jet at the LHC are studied under realistic assumptions, including effects of the final-state parton showering.

High-precision measurements by the ATLAS Collaboration are presented of inclusive $W^+\to\ell^+\nu$, $W^-\to\ell^-\bar{\nu}$ and $Z/\gamma^*\to\ell\ell$ ($\ell=e,\mu$) Drell-Yan production cross sections at the LHC. The data were collected in proton-proton collisions at $\sqrt{s} = 7$ TeV with an integrated luminosity of 4.6 fb$^{-1}$. Differential $W^+$ and $W^-$ cross sections are measured in a lepton pseudorapidity range $|\eta_{\ell}| = 2.5$. Differential $Z/\gamma^*$ cross sections are measured as a function of the absolute dilepton rapidity, for $|y_{\ell\ell}| < 3.6$, for three intervals of dilepton mass, $m_{\ell\ell}$, extending from 46 to 150 GeV. The integrated and differential electron- and muon-channel cross sections are combined and compared to theoretical predictions using recent sets of parton distribution functions. The data, together with the final inclusive $e^{\pm}p$ scattering cross-section data from H1 and ZEUS, are interpreted in a next-to-next-to-leading-order QCD analysis, and a new set of parton distribution functions, ATLAS-epWZ16, is obtained. The ratio of strange-to-light sea-quark densities in the proton is determined more accurately than in previous determinations based on collider data only, and is established to be close to unity in the sensitivity range of the data. A new measurement of the CKM matrix element $|V_{cs}|$ is also provided.

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light quarks and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the determination of the gluon. We explore the implications of NNPDF3.1 for LHC phenomenology at Run II, compare with recent LHC measurements at 13 TeV, provide updated predictions for Higgs production cross-sections and discuss the strangeness and charm content of the proton in light of our improved dataset and methodology. The NNPDF3.1 PDFs are delivered for the first time both as Hessian sets, and as optimized Monte Carlo sets with a compressed number of replicas.

Ratios of top-quark pair to Z-boson cross sections measured from proton-proton collisions at the LHC centre-of-mass energies of s=13 TeV, 8 TeV, and 7 TeV are presented by the ATLAS Collaboration. Single ratios, at a given s for the two processes and at different s for each process, as well as double ratios of the two processes at different s, are evaluated. The ratios are constructed using previously published ATLAS measurements of the tt¯ and Z-boson production cross sections, corrected to a common phase space where required, and a new analysis of Z → ℓ⁺ℓ⁻ where ℓ = e, μ at s=13 TeV performed with data collected in 2015 with an integrated luminosity of 3.2 fb⁻¹. Correlations of systematic uncertainties are taken into account when evaluating the uncertainties in the ratios. The correlation model is also used to evaluate the combined cross section of the Z → e⁺e⁻ and the Z → μ⁺μ⁻ channels for each s value. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data demonstrate significant power to constrain the gluon distribution function for the Bjorken-x values near 0.1 and the light-quark sea for x < 0.02.[Figure not available: see fulltext.]

We present an unbiased determination of the charm content of the proton, in which the charm parton distribution function (PDF) is parametrized on the same footing as the light quarks and the gluon in a global PDF analysis. This determination relies on the NLO calculation of deep-inelastic structure functions in the FONLL scheme, generalized to account for massive charm-initiated contributions. When the EMC charm structure function dataset is included, it is well described by the fit, and PDF uncertainties in the fitted charm PDF are significantly reduced. We then find that the fitted charm PDF vanishes within uncertainties at a scale Q∼ 1.6 GeV for all x≲ 0.1 , independent of the value of mc used in the coefficient functions. We also find some evidence that the charm PDF at large x≳ 0.1 and low scales does not vanish, but rather has an “intrinsic” component, very weakly scale dependent and almost independent of the value of mc, carrying less than 1 % of the total momentum of the proton. The uncertainties in all other PDFs are only slightly increased by the inclusion of fitted charm, while the dependence of these PDFs on mc is reduced. The increased stability with respect to mc persists at high scales and is the main implication of our results for LHC phenomenology. Our results show that if the EMC data are correct, then the usual approach in which charm is perturbatively generated leads to biased results for the charm PDF, though at small x this bias could be reabsorbed if the uncertainty due to the charm mass and missing higher orders were included. We show that LHC data for processes, such as high pT and large rapidity charm pair production and Z+ c production, have the potential to confirm or disprove the implications of the EMC data.

Small-$x$ logarithmic enhancements arising from high-energy gluon emissions affect both the evolution of collinearly-factorized parton densities and partonic coefficient functions. With the higher collider energy reached by the LHC, the prospect of a future high-energy collider, and the recent deep-inelastic scattering (DIS) results at small-$x$ from HERA, providing phenomenological tools for performing small-$x$ resummation has become of great relevance. In this paper we discuss a framework to perform small-$x$ resummation for both parton evolution and partonic coefficient functions and we describe its implementation in a computer code named High-Energy Large Logarithms (HELL). We present resummed and matched results for the DGLAP splitting functions and, as a proof of principle, for the massless structure functions in DIS.

Measurements of the and production cross sections (where ) in proton–proton collisions at are presented using data recorded by the ATLAS experiment at the Large Hadron Collider, corresponding to a total integrated luminosity of 81 pb−1. The total inclusive -boson production cross sections times the single-lepton-flavour branching ratios are and for and , respectively. The total inclusive _Z_-boson production cross section times leptonic branching ratio, within the invariant mass window , is . The , , and _Z_-boson production cross sections and cross-section ratios within a fiducial region defined by the detector acceptance are also measured. The cross-section ratios benefit from significant cancellation of experimental uncertainties, resulting in and . Theoretical predictions, based on calculations accurate to next-to-next-to-leading order for quantum chromodynamics and to next-to-leading order for electroweak processes and which employ different parton distribution function sets, are compared to these measurements.

We derive a kinematic condition on the resolution of intrinsic charm and
discuss phenomenological consequences.

Production cross-sections of prompt charm mesons are measured with the first data from pp collisions at the LHC at a centre-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 4.98 ± 0.19 pb−1 collected by the LHCb experiment. The production cross-sections of D
0, D
+, D
s
+, and D
*+ mesons are measured in bins of charm meson transverse momentum, p
T, and rapidity, y, and cover the range 0 < p
T < 15GeV/c and 2.0 < y < 4.5. The inclusive cross-sections for the four mesons, including charge conjugation, within the range of 1 < p
T < 8 GeV/c are found to be
$$ \begin{array}{l}\sigma \left( pp\to {D}^0X\right)=2460\pm 3\pm 130\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}^{+}X\right)=1000\pm 3\pm 110\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}_s^{+}X\right)=460\pm 13\pm 100\;\upmu \mathrm{b}\hfill \\ {}\sigma \left( pp\to {D}^{\ast +}X\right)=880\pm 5\pm 140\;\upmu \mathrm{b}\hfill \end{array} $$
where the uncertainties are due to statistical and systematic uncertainties, respectively.

We present a review of the state-of-the-art of our understanding of the
intrinsic charm and bottom content of the nucleon. We discuss theoretical
calculations, constraints from global analyses, and collider observables
sensitive to the intrinsic heavy quark distributions. A particular emphasis is
put on the potential of a high-energy and high-luminosity fixed target
experiment using the LHC beams (AFTER@LHC) to search for intrinsic charm.

We present a new global QCD analysis of parton distribution functions,
allowing for possible nonperturbative or intrinsic charm (IC) contributions in
the nucleon inspired by light-front models. The analysis makes use of the full
range of available high energy scattering data for Q^2 > 1 GeV^2 and W^2 > 3.5
GeV^2, including SLAC proton and deuteron deep-inelastic scattering cross
sections that were excluded in previously global analyses. The SLAC data in
particular place more stringent constraints on the momentum carried by IC, with
_IC < 0.1% at the 5-sigma level. We also critically assess the impact of
older EMC measurements of F_2c at large x, which favor a nonzero IC, _IC =
0.13 +- 0.04%, but have a very large chi^2 value.

We perform a comprehensive analysis of the role of nonperturbative (or
intrinsic) charm in the nucleon, generated through Fock state expansions of the
nucleon wave function involving five-quark virtual states represented by
charmed mesons and baryons. We consider contributions from a variety of charmed
meson-baryon states and find surprisingly dominant effects from the (Dbar^{*0}
Lambda_c+) configuration. Particular attention is paid to the existence and
persistence of high-x structure for intrinsic charm, and the x dependence of
the c-cbar asymmetry predicted in meson-baryon models. We discuss how studies
of charmed baryons and mesons in hadronic reactions can be used to constrain
models, and outline future measurements that could further illuminate the
intrinsic charm component of the nucleon.

We study the possibility of intrinsic (non-perturbative) charm in parton
distribution functions (PDF) of the proton, within the context of the CT10
next-to-next-to-leading order (NNLO) global analysis. Three models for the
intrinsic charm (IC) quark content are compared: (i) $\hat{c}(x) = 0$ (zero-IC
model); (ii) $\hat{c}(x)$ is parametrized by a valence-like parton distribution
(BHPS model); (iii) $\hat{c}(x)$ is parametrized by a sea-like parton
distribution (SEA model). In these models, the intrinsic charm content,
$\hat{c}(x)$, is included in the charm PDF at the matching scale $Q_c=m_c=1.3$
GeV. The best fits to data are constructed and compared. Correlations between
the value of $m_c$ and the amount of IC are also considered.

We present a model based on the concept of saturation for small Q2 and small x. With only three parameters we achieve a good description of all deep inelastic scattering data below x=0.01. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.

The postulate that ordinary hadrons contain intrinsic charm-quark states (such as |uudcc̅ 〉 in the proton) at the 1% level is shown to explain two sets of unexpected experimental results: (1) the copious diffractive production of charmed hadrons at large longitudinal momentum in high-energy proton-nucleon and pion-nucleon collisions, and (2) the anomalously large number of same-sign dimuon events observed in deep-inelastic neutrino reactions. We also predict cross sections for open b and t production for high-energy hadron-hadron collisions.

Measurements of the ratio of Drell-Yan yields from an 800 GeV/c proton beam incident on liquid hydrogen and deuterium targets are reported. Approximately 360 000 Drell-Yan muon pairs remained after all cuts on the data. From these data, the ratio of down antiquark (d̅ ) to up (ū) antiquark distributions in the proton sea is determined over a wide range in Bjorken-x. These results confirm previous measurements by E866 and extend them to lower x. From these data, (d̅ -ū) and ∫(d̅ -ū)dx are evaluated for 0.015<x<0.35. These results are compared with parametrizations of various parton distribution functions, models and experimental results from NA51, NMC and HERMES.

Charm production at the LHC in pp collisions at sqrt(s)=7 TeV is studied with
the LHCb detector. The decays D0 -> K- pi+, D+ -> K- pi+ pi+, D*+ -> D0(K- pi+)
pi+, D_s+ -> phi(K- K+) pi+, Lambda_c+ -> p K- pi+, and their charge conjugates
are analysed in a data set corresponding to an integrated luminosity of 15
nb^{-1}. Differential cross-sections dsigma/dp_T are measured for prompt
production of the five charmed hadron species in bins of transverse momentum
and rapidity in the region 0 < p_T < 8 GeV/c and 2.0 < y < 4.5. Theoretical
predictions are compared to the measured differential cross-sections. The
integrated cross-sections of the charm hadrons are computed in the above p_T-y
range, and their ratios are reported. A combination of the five integrated
cross-section measurements gives
sigma(c\bar{c})_{p_T < 8 GeV/c, 2.0 < y < 4.5} = 1419 +/- 12 (stat) +/- 116
(syst) +/- 65 (frag) microbarn,
where the uncertainties are statistical, systematic, and due to the
fragmentation functions.

We present a next-to-next-to-leading order (NNLO) realization of a general
quark mass scheme (S-ACOT-$\chi$) in deep inelastic scattering and explore the
impact of NNLO terms on heavy-quark structure functions $F_{2,L}^{c}(x,Q)$. An
amended QCD factorization theorem for DIS is discussed that validates the
S-ACOT-$\chi$ scheme to all orders in the QCD coupling strength. As a new
feature, kinematical constraints on collinear production of heavy quarks that
are crucial near the heavy-quark threshold are included in the amended
factorization theorem. An algorithmic procedure is outlined for implementing
this scheme at NNLO by using mass-dependent and massless results from
literature. At two loops in QCD cut diagrams, the S-ACOT-$\chi$ scheme reduces
scale dependence of heavy-quark DIS cross sections as compared to the
fixed-flavor number scheme.

Expectations for the momentum distribution of nonperturbative charm and bottom quarks in the proton are derived from a variety of models for the Fock space wave function on the light cone.

The separation of the connected and disconnected sea partons, which were uncovered in the Euclidean path-integral formulation of the hadronic tensor, is accommodated with the CT18 parametrization of the global analysis of the parton distribution functions (PDFs). This is achieved with the help of the distinct small x x behaviors of these two sea parton components and the constraint from the lattice calculation of the ratio of the strange momentum fraction to that of the {\bar u} u ‾ or {\bar d} d ‾ in the disconnected insertion. This allows lattice calculations of separate flavors in both the connected and disconnected insertions to be directly compared with the global analysis results term by term.

We report on the W and Z/γ* differential and total cross sections as well as the W+/W− and (W++W−)/(Z/γ*) cross section ratios measured by the STAR experiment at RHIC in p+p collisions at s=500 GeV and 510 GeV. The cross sections and their ratios are sensitive to quark and antiquark parton distribution functions. In particular, at leading order, the W cross section ratio is sensitive to the d¯/u¯ ratio. These measurements were taken at high Q2∼MW2,MZ2 and can serve as input into global analyses to provide constraints on the sea quark distributions. The results presented here combine three STAR datasets from 2011, 2012, and 2013, accumulating an integrated luminosity of 350 pb−1. We also assess the expected impact that our W+/W− cross section ratios will have on various quark distributions, and find sensitivity to the u¯−d¯ and d¯/u¯ distributions.

Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross-section data. Definitions of the PDFs and their relations to high-energy cross sections are reviewed. The focus is on the PDFs in protons, but PDFs in nuclei are also discussed. The standard statistical treatment needed to fit the PDFs to data using the Hessian method is reviewed in some detail. Tests are discussed that critically examine whether the needed assumptions are indeed valid. Also presented are some ideas of what one can do in case tests indicate that the assumptions fail.

The light-quark flavor dependence of the proton sea has been of great interest for many years because of its close connection with non-perturbative effects. One hypothesis is that the sea arises from the pion cloud of the proton. We make precise predictions based on the pion cloud idea for an anticipated future measurement. This is achieved by applying light cone perturbation theory and experimental constraints to a chiral Lagrangian so that the relevant Fock-space components of the nucleon wave function are computed with reasonable accuracy. Existing experimental information regarding the light flavor sea is studied, and predictions, including uncertainties, for future experimental results are provided. Future experiments will either confirm or rule out the idea that the pion cloud provides the flavor dependence of the proton's sea quark distribution, and have profound implications for understanding the nucleon-nucleon force.

We determine a new set of parton distribution functions (ABMP16), the strong coupling constant $\alpha_s$ and the quark masses $m_c$, $m_b$ and $m_t$ in a global fit to next-to-next-to-leading order (NNLO) in QCD. The analysis uses the $\overline{\mathrm{MS}}$ scheme for $\alpha_s$ and all quark masses and is performed in the fixed-flavor number scheme for $n_f=3, 4, 5$. Essential new elements of the fit are the combined data from HERA for inclusive deep-inelastic scattering (DIS), data from the fixed-target experiments NOMAD and CHORUS for neutrino-induced DIS, and data from Tevatron and the LHC for the Drell-Yan process and the hadro-production of single-top and top-quark pairs. The theory predictions include new improved approximations at NNLO for the production of heavy quarks in DIS and for the hadro-production of single-top quarks. The description of higher twist effects relevant beyond the leading twist collinear factorization approximation is refined. At NNLO we obtain the value $\alpha_s^{(n_f=5)}(M_Z) = 0.1147 \pm 0.0008$.

We present a new set of leading twist parton distribution functions, referred to as "CJ15", which take advantage of developments in the theoretical treatment of nuclear corrections as well as new data. The analysis includes for the first time data on the free neutron structure function from Jefferson Lab, and new high-precision charged lepton and W-boson asymmetry data from Fermilab. These significantly reduce the uncertainty on the d/u ratio at large values of x and provide new insights into the partonic structure of bound nucleons.

Filling a gap in the current literature, this book is the first entirely dedicated to high energy QCD including parton saturation. It presents groundbreaking progress on the subject and describes many of the problems at the forefront of research, bringing postgraduate students, theorists and advanced experimentalists up to date with the current status of the field. A broad range of topics in high energy QCD are covered, most notably on the physics of parton saturation and the Color Glass Condensate (CGC). The material is presented in a pedagogical way, with numerous examples and exercises. Discussion ranges from the quasi-classical McLerran-Venugopalan model to the linear and non-linear BFKL/BK/JIMWLK small-x evolution equations. The authors adopt both a theoretical and experimental outlook and present the physics of strong interactions in a universal way, making it useful to physicists from various sub-communities and applicable to processes studied at high energy accelerators around the world. A selection of color figures is available online at www.cambridge.org/9780521112574.

Quantum electrodynamics and electroweak corrections are an important
ingredient for many theoretical predictions at the LHC. This paper introduces
APFEL, a new PDF evolution library which allows for the first time to perform
DGLAP evolution up to NNLO in QCD and to LO in QED, in the
variable-flavor-number scheme and with either pole or MSbar heavy quark masses.
APFEL consistently accounts for the QED corrections to the evolution of quark
and gluon PDFs and for the contribution from the photon PDF in the proton. The
coupled QCD+QED equations are solved in x-space by means of higher order
interpolation, followed by Runge-Kutta solution of the resulting discretized
evolution equations. APFEL is based on an innovative methodology for the
sequential solution of the QCD and QED evolution equations and their
combination, leading to a flexibility that allows to explore different options
for the treatment of subleading terms. APFEL has been validated by means of
detailed benchmark comparisons with other publicly available QCD and QED PDF
evolution tools. Written in Fortran77, APFEL can also be easily used via the
C/C++ and Python interfaces, and is publicly available from the HepForge
repository.

Heavy flavour production is an important quantum chromodynamics (QCD) process both in its own right and as a key component of precision global QCD analysis. Apparent disagreements between fixed-flavour scheme calculations of b-production rate with experimental measurements in hadro-, lepto- and photo-production provide new impetus for a thorough examination of the theory and phenomenology of this process. We review existing methods of calculation and place them in the context of the general perturbative QCD framework of Collins. A distinction is drawn between scheme dependence and implementation issues related to quark mass effects near threshold. We point out a so far overlooked kinematic constraint on the threshold behaviour, which greatly simplifies the variable flavour number scheme. This obviates the need for the elaborate existing prescriptions and leads to robust predictions. It can facilitate the study of current issues on heavy flavour production as well as precision global QCD analysis.

A method to facilitate the consistent inclusion of cross-section measurements based on complex final-states from HERA, TEVATRON
and the LHC in proton parton density function (PDF) fits has been developed. This can be used to increase the sensitivity
of LHC data to deviations from Standard Model predictions. The method stores perturbative coefficients of NLO QCD calculations
of final-state observables measured in hadron colliders in look-up tables. This allows the aposteriori inclusion of parton
density functions (PDFs), and of the strong coupling, as well as the aposteriori variation of the renormalisation and factorisation
scales in cross-section calculations. The main novelties in comparison to original work on the subject are the use of higher-order
interpolation of Lagrangian form, which substantially improves the trade-off between accuracy and memory use, and a CPU and
computer memory optimised way to construct and store the look-up table using modern software tools. It is demonstrated that
a sufficient accuracy on the cross-section calculation can be achieved with reasonably small look-up table size by using the
examples of jet production and electro-weak boson (Z,W) production in proton-proton collisions at a center-of-mass energy of 14TeV at the LHC. The use of this technique in PDF
fitting is demonstrated in a PDF-fit to HERA data and simulated LHC jet cross-sections as well as in a study of the jet cross-section
uncertainties at various centre-of-mass energies.

We discuss a general framework for the inclusion of heavy quark mass contributions to deep-inelastic structure functions and their perturbative matching to structure functions computed in variable-mass schemes. Our approach is based on the so-called FONLL method, previously introduced and applied to heavy quark hadroproduction and photoproduction. We define our framework, provide expressions up to second order in the strong coupling, and use them to construct matched expressions for structure functions up to NNLO. After checking explicitly the consistency of our results, we perform a study of the phenomenological impact of heavy quark terms, and compare results obtained at various perturbative orders, and with various prescriptions for the treatment of subleading terms, specifically those related to threshold behaviour. We also consider the heavy quark structure function F2c and discuss issues related to the presence of mass singularities in their coefficient functions.

Recent data give unexpectedly large cross-sections for charmed particle production at high xF in hadron collisions. This may imply that the proton has a non-negligible uudc Fock component. The interesting consequences of such a hypothesis are explored.

We present the program Top++ for the numerical evaluation of the total
inclusive cross-section for producing top quark pairs at hadron colliders. The
program calculates the cross-section in a) fixed order approach with exact NNLO
for $q\bar q\to t\bar t+X, qq\to t\bar t+X, q\bar q'\to t\bar t+X, qq'\to t\bar
t+X$ and through approximate NNLO for $gg\to t\bar t+X$ and b) by including
soft-gluon resummation for the hadronic cross-section in Mellin space with full
next-to-next-to-leading logarithmic accuracy. The program offers the user
significant flexibility through the large number (31) of available options.
Top++ is written in C++. It has a very simple to use interface that is
intuitive and directly reflects the physics. The running of the program
requires no programing experience from the user.

The existence of the five-quark Fock states for the intrinsic charm quark in the nucleons was suggested some time ago, but conclusive evidence is still lacking. We generalize the previous theoretical approach to the light-quark sector and study possible experimental signatures for such five-quark states. In particular, we compare the d-ū and ū + d-s-s data with the calculations based on the five-quark Fock states. The qualitative agreement between the data and the calculations is interpreted as evidence for the existence of the intrinsic light-quark sea in the nucleons. The probabilities for the |uuduū and |uuddd Fock states are also extracted.

A detailed proof of hard scattering factorization is given with the inclusion of heavy quark masses. Although the proof is explicitly given for deep-inelastic scattering, the methods apply more generally The power-suppressed corrections to the factorization formula are uniformly suppressed by a power of \Lambda/Q, independently of the size of heavy quark masses, M, relative to Q. Comment: 56 pages, 13 figures; RevTeX & epsf

A unified QCD formulation of leptoproduction of massive quarks in charged current and neutral current processes is described. This involves adopting consistent factorization and renormalization schemes which encompass both vector-boson-gluon-fusion (flavor creation) and vector-boson-massive-quark-scattering (flavor excitation) production mechanisms. It provides a framework which is valid from the threshold for producing the massive quark (where gluon-fusion is dominant) to the very high energy regime when the typical energy scale \mu is much larger than the quark mass m_Q (where the quark-scattering should be prevalent). This approach effectively resums all large logarithms of the type (alpha_s(mu) log(mu^2/m_Q^2)^n which limit the validity of existing fixed-order calculations to the region mu ~ O(m_Q). We show that the (massive) quark-scattering contribution (after subtraction of overlaps) is important in most parts of the (x, Q) plane except near the threshold region. We demonstrate that the factorization scale dependence of the structure functions calculated in this approach is substantially less than those obtained in the fixed-order calculations, as one would expect from a more consistent formulation. Comment: LaTeX format, 29 pages, 11 figures. Revised to make auto-TeX-able

Existing calculations of heavy quark production in charged-current and neutral current lepton-hadron scattering are formulated differently because of the artificial distinction of ``light'' and ``heavy'' quarks made in the traditional approach. A proper QCD formalism valid for a wide kinematic range from near threshold to energies much higher then the quark mass should treat these processes in a uniform way. We formulate a unified approach to both types of leptoproduction processes based on the conventional factorization theorem. In this paper, we present the general framework with complete kinematics appropriate for arbitrary masses, emphasizing the simplifications provided by the helicity formalism. We illustrate this approach with an explicit calculation of the leading order contribution to the quark structure functions with general masses. This provides the basis for a complete QCD analysis of charged current and neutral current leptoproduction of charm and bottom quarks to be presented in subsequent papers. Comment: LaTeX format, 28 pages, 7 figures. Revised to make auto-TeX-able

We investigate a simplified version of the ACOT prescription for calculating deeply inelastic scattering from Q^2 values near the squared mass M_H^2 of a heavy quark to Q^2 much larger than M_H^2.