Global Parton Distribution Functions Research Articles

Combining QED and approximate ${\rm N}^3$LO QCD corrections in a global PDF fit: MSHT20qed_an3lo PDFs

We present the MSHT20qed_an3lo parton distribution functions (PDFs). These result from the first global PDF analysis to combine QED and approximate N^3N3LO (aN^3N3LO) QCD corrections in the theoretical calculation of the PDF evolution and cross sections entering the fit. We examine the PDF impact, and find that the effect of QED is relatively mild in comparison to the aN^3N3LO corrections, although it should still be accounted for at the level of precision now required. These QED corrections are in addition found to roughly factorise from the QCD corrections; that is, their relative impact on the PDFs is roughly the same at NNLO and aN^3N3LO. The fit quality exhibits a very small deterioration at aN^3N3LO upon the inclusion of QED corrections, which is rather smaller than the deterioration observed at NNLO in QCD. The impact on several cross-sections at N^3N3LO is also examined, including the Higgs cross sections at N^3N3LO. Finally, a LO in QCD fit that includes QED corrections is also presented: the MSHT20qed_an3lo set.

Hide and seek: how PDFs can conceal new physics

The interpretation of LHC data, and the assessment of possible hints of new physics, require the precise knowledge of the proton structure in terms of parton distribution functions (PDFs). We present a systematic methodology designed to determine whether and how global PDF fits might inadvertently ‘fit away’ signs of new physics in the high-energy tails of the distributions. We showcase a scenario for the High-Luminosity LHC, in which the PDFs may completely absorb such signs of new physics, thus biasing theoretical predictions and interpretations. We discuss strategies to single out the effects in this scenario, and disentangle the inconsistencies that stem from them. Our study brings to light the synergy between the high luminosity programme at the LHC and future low-energy non-LHC measurements of large-x sea quark distributions. The analysis code used in this work is made public so that any users can test the robustness of the signal associated to a given BSM model against absorption by the PDFs.

Generalized parton distributions through universal moment parameterization: non-zero skewness case

We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs) and deeply virtual Compton scattering (DVCS) measurements. Following the previous work where we parameterize GPDs in terms of their moments, we extend the framework to allow for the global analysis at non-zero skewness. Together with the constraints at zero skewness, we fit GPDs to global DVCS measurements from both the recent JLab and the earlier Hadron-Electron Ring Accelerator (HERA) experiments with two active quark flavors and leading order QCD evolution. With certain choices of empirical constraints, both sea and valence quark distributions are extracted with the combined inputs, and we present the quark distributions in the proton correspondingly. We also discuss how to extend the framework to accommodate more off-forward constraints beyond the small ξ expansion, especially the lattice calculated GPDs.

Impact of lattice strangeness asymmetry data in the CTEQ-TEA global analysis

We study the impact of lattice data on the determination of the strangeness asymmetry distribution ${s}_{\ensuremath{-}}(x)\ensuremath{\equiv}s(x)\ensuremath{-}\overline{s}(x)$ in the general CTEQ-TEA global analysis of parton distribution functions (PDFs) of the proton. Firstly, we find that allowing a nonvanishing ${s}_{\ensuremath{-}}(x)$, at the initial ${Q}_{0}=1.3\text{ }\text{ }\mathrm{GeV}$ scale, in a global PDF analysis leads to a CT18As fit with similar quality to CT18A. Secondly, including the lattice data in the CT18As_Lat fit greatly reduces the ${s}_{\ensuremath{-}}$-PDF error band size in the large-$x$ region. To further reduce its error would require more precise lattice data, extended to smaller $x$ values. We take ATLAS 7 TeV $W$ and $Z$ production data, SIDIS dimuon production data, ${F}_{3}$ structure function data, E866 NuSea data, and E906 SeaQuest data as examples to illustrate the implication of CT18As and CT18As_Lat fits. The parametrization dependence for PDF ratio $(s+\overline{s})/(\overline{u}+\overline{d})(x)$ is analyzed with CT18As2 and CT18As2_Lat fits as results.

Inclusive production cross sections at N3LO

We present for the first time the inclusive cross section for associated Higgs boson production with a massive gauge boson at next-to-next-to-next-to-leading order in QCD. Furthermore, we introduce n3loxs, a public, numerical program for the evaluation of inclusive cross sections at the third order in the strong coupling constant. Our tool allows to derive predictions for charged- and neutral-current Drell-Yan production, gluon- and bottom-quark-fusion Higgs boson production and Higgs boson associated production with a heavy gauge boson. We discuss perturbative and parton distribution function (PDF) uncertainties of the aforementioned processes. We perform a comparison of global PDF sets for a variety of process including associated Higgs boson production and observe 1σ deviations among predictions for several processes.

The NNLO QCD analysis of gluon density at small-x

In this paper, a next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) calculation of gluon distribution function at small-[Formula: see text] is presented. The gluon distribution function is explored analytically in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi approach by a Taylor expansion at small-[Formula: see text] as two first-order partial differential equations in two variables: Bjorken [Formula: see text] and [Formula: see text][Formula: see text]. We have solved the system of equations at LO, NLO and NNLO, respectively, by Lagrange’s method. The resulting analytical expressions are compared with the available global parton distribution function fits as well as with the results of the Block–Durand–McKay model. We have further performed an [Formula: see text] test to check the compatibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small-[Formula: see text] region.

The PDF4LHC21 combination of global PDF fits for the LHC Run III* *We dedicate this paper to the memory of James Stirling, Dick Roberts and Jon Pumplin, all of whom sadly died in the past few years. All three were instrumental in the development and evolution of PDF fitting, Jon for the CTEQ-TEA collaboration and James and Dick for the

A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton–hadron and hadron–hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond.

Measurement of the W boson mass

The W boson mass is measured using proton-proton collision data at sqrt{s} = 13 TeV corresponding to an integrated luminosity of 1.7 fb−1 recorded during 2016 by the LHCb experiment. With a simultaneous fit of the muon q/pT distribution of a sample of W → μν decays and the ϕ* distribution of a sample of Z → μμ decays the W boson mass is determined to bemw=80354±23stat±10exp±17theory±9PDFMeV,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ {m}_w=80354\\pm {23}_{\\mathrm{stat}}\\pm {10}_{\\mathrm{exp}}\\pm {17}_{\\mathrm{theory}}\\pm {9}_{\\mathrm{PDF}}\\mathrm{MeV}, $$\\end{document}where uncertainties correspond to contributions from statistical, experimental systematic, theoretical and parton distribution function sources. This is an average of results based on three recent global parton distribution function sets. The measurement agrees well with the prediction of the global electroweak fit and with previous measurements.

Probing nucleon strange and charm distributions with lattice QCD

We present the first lattice-QCD calculation of the unpolarized strange and charm parton distribution functions using large-momentum effective theory. We use a lattice ensemble with ($2+1+1$) flavors of highly improved staggered quarks generated by the MILC Collaboration, with lattice spacing $a\ensuremath{\approx}0.12\text{ }\text{ }\mathrm{fm}$ and ${M}_{\ensuremath{\pi}}\ensuremath{\approx}310\text{ }\text{ }\mathrm{MeV}$, and clover valence fermions with two valence pion masses: 310 and 690 MeV. We use momentum-smeared sources to improve the signal up to nucleon boost momentum ${P}_{z}=2.15\text{ }\text{ }\mathrm{GeV}$, and determine nonperturbative renormalization factors in regularization independent momentum subtraction scheme. We compare our lattice results with the matrix elements obtained from matching the parton distribution functions (PDFs) from CT18NNLO and NNPDF3.1NNLO global fits. Our data support the assumptions of strange-antistrange and charm-anticharm symmetry that are commonly used in global PDF fits.

Self-consistent determination of proton and nuclear PDFs at the Electron Ion Collider

We quantify the impact of unpolarized lepton-proton and lepton-nucleus inclusive deep-inelastic scattering (DIS) cross section measurements from the future Electron-Ion Collider (EIC) on the proton and nuclear parton distribution functions (PDFs). To this purpose, we include neutral- and charged-current DIS pseudodata in a self-consistent set of proton and nuclear global PDF determinations based on the NNPDF methodology. We demonstrate that the EIC measurements will reduce the uncertainty of the light quark PDFs of the proton at large values of the momentum fraction $x$ and, more significantly, of the quark and gluon PDFs of heavy nuclei, especially at small and large $x$. We illustrate the implications of the improved precision of nuclear PDFs for the interaction of ultrahigh energy cosmic neutrinos with matter.

Nucleon gluon distribution function from 2 + 1 + 1-flavor lattice QCD

The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-[Formula: see text] region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that access the [Formula: see text]-dependence of the gluon unpolarized PDF of the nucleon. The lattice calculation is carried out with nucleon momenta up to 2.16 GeV, lattice spacing [Formula: see text] fm, and with valence pion masses of 310 and 690 MeV. We use reduced Ioffe-time distributions to cancel the renormalization and implement a one-loop perturbative pseudo-PDF gluon matching. We neglect mixing of the gluon operator with the quark singlet sector. Our matrix-element results in coordinate space are consistent with those obtained from the global PDF fits of CT18 NNLO and NNPDF3.1 NNLO. Our fitted gluon PDFs at both pion masses are consistent with global fits in the [Formula: see text] region.

Very low x gluon density determined by LHCb exclusive J/ψ data

The low $x$ behaviour of the gluon density $xg(x,\mu^2)$ at scale $\mu^2=2.4$ GeV$^2$ is determined using exclusive $J/\psi$ production data from HERA and LHCb within the framework of collinear factorisation at next-to-leading order (NLO). It is shown that in the interval $3\times 10^{-6} < x <10^{-3}$ the gluon distribution function grows as $xg(x,\mu^2)\propto x^{-\lambda}$ with $\lambda=0.135\pm 0.006 $. The impact this experimental data will have for the global parton distribution function (PDF) analyses in this low $x$ domain is quantified. No indication in favour of parton density saturation is observed.

How to include exclusive J/ψ production data in global PDF analyses

We compare the cross section for exclusive $J/\psi$ photoproduction calculated at NLO in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double counting we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. However, at low $x$ the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of $x$, $10^{-6}<x<10^{-2}$, at a fixed low scale.

Parton distributions with theory uncertainties: general formalism and first phenomenological studies

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology. In addition, we also compare the results based on the theory covariance matrix formalism to those obtained by performing PDF determinations based on different scale choices.

Parton Distribution Functions and Lattice QCD

Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken-x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $ \overline {{\rm{MS}}} $ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large-x global PDF fits are also discussed.

Impact of the heavy-quark matching scales in PDF fits

We investigate the impact of displaced heavy-quark matching scales in a global fit. The heavy-quark matching scale mu _{m} determines at which energy scale mu the QCD theory transitions from N_{F} to N_{F}+1 in the variable flavor number scheme (VFNS) for the evolution of the parton distribution functions (PDFs) and strong coupling alpha _S(mu ). We study the variation of the matching scales, and their impact on a global PDF fit of the combined HERA data. As the choice of the matching scale mu _{m} effectively is a choice of scheme, this represents a theoretical uncertainty; ideally, we would like to see minimal dependence on this parameter. For the transition across the charm quark (from N_{F}=3 to 4), we find a large mu _m=mu _{c} dependence of the global fit chi ^2 at NLO, but this is significantly reduced at NNLO. For the transition across the bottom quark (from N_{F}=4 to 5), we have a reduced mu _{m}=mu _b dependence of the chi ^2 at both NLO and NNLO as compared to the charm. This feature is now implemented in xFitter 2.0.0, an open source QCD fit framework.

A determination of the charm content of the proton: The NNPDF Collaboration.

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 Qsim 1.6 GeV for all xlesssim 0.1, independent of the value of m_c used in the coefficient functions. We also find some evidence that the charm PDF at large xgtrsim 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 m_c, 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 m_c is reduced. The increased stability with respect to m_c 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 p_T and large rapidity charm pair production and Z+c production, have the potential to confirm or disprove the implications of the EMC data.

Exclusive J/ψ and ϒ photoproduction and the low x gluon

We study exclusive vector meson photoproduction, with or ϒ, at next-to-leading order (NLO) in collinear factorisation, in order to examine what may be learnt about the gluon distribution at very low x. We examine the factorisation scale dependence of the predictions. We argue that, using knowledge of the NLO corrections, terms enhanced by a large can be reabsorbed in the LO part by a choice of the factorisation scale. (In these exclusive processes ξ takes the role of Bjorken-x.) Then, the scale dependence coming from the remaining NLO contributions has no enhancements. As a result, we find that predictions for the amplitude of ϒ production are stable to within about ±15%. This will allow data for the exclusive process at the Large Hadron Collider (LHC), particularly from LHCb, to be included in global parton analyses to constrain the gluon parton distribution function (PDF) down to Moreover, the study of exclusive photoproduction indicates that the gluon density found in the recent global PDF analyses is too small at low x and low scales.

Standard Model measurements with the ATLAS detector

Various Standard Model measurements have been performed in proton-proton collisions at a centre-of-mass energy of √ s = 7 and 8 TeV using the ATLAS detector at the Large Hadron Collider. A review of a selection of the latest results of electroweak measurements, W/Z production in association with jets, jet physics and soft QCD is given. Measurements are in general found to be well described by the Standard Model predic- tions. been performed in proton-proton collisions at a centre-of-mass energy of √ s = 7 and 8 TeV using the ATLAS detector (1) at the LHC. These allow for precision tests of the electroweak dynamics of the Standard Model, but also challenge next-to-next-to-leading-order predictions. Differences between measurements and Standard Model predictions could prove evidence for new phenomena. Recent Quantum Chromo Dynamics (QCD) results highlight the importance of precision QCD measurements for improving state-of-the-art theoretical tools and searching for new physics. A selection of the latest results of electroweak measurements, W/Z production in association with jets, jet physics and soft QCD is reported. These consist of the measurement of the WW cross section, first evidence of the electroweak production of W ± W ± jj , and electroweak Zj jproduction. Measurements are in general found to be well described by the Standard Model predictions. Measurements of differential produc- tion cross sections of a Z boson in association with b-jets, the production cross section of the W boson in association with jets as well as the ratio of the production cross sections for W and Z bosons in association with jets are presented. The measurements are compared to next-to-leading-order pertur- bative QCD calculations and to predictions from different Monte Carlo (MC) generators implement- ing leading-order matrix elements supplemented by parton showers. Various inclusive, differential or double differential jet measurements are presented. The dominant experimental uncertainty on these measurements comes from the jet energy scale. Next-to-leading order QCD calculations corrected to account for non-perturbative effects are compared to the measurements. A good agreement between the data and the theoretical predictions based on most of the global parton distribution functions is found over the full kinematic range, covering almost seven orders of magnitude in the measured cross-section values. A measurement of charged-particle distributions sensitive to the properties of

Uncertainties in determining parton distributions at largex

We critically examine uncertainties in parton distribution functions (PDFs) at large x arising from nuclear effects in deuterium F2 structure function data. Within a global PDF analysis, we assess the impact on the PDFs from uncertainties in the deuteron wave function at short distances and nucleon off-shell effects, the use of relativistic kinematics, as well as the use of less a restrictive parametrization of the d/u ratio. We find that in particular the d-quark and gluon PDFs vary significantly with the choice of nuclear model. We highlight the impact of these uncertainties on the determination of the neutron structure function, and on W boson production and parton luminosity at the Tevatron and the LHC. Finally, we discuss prospects for new measurements sensitive to the d-quark and gluon distributions but insensitive to nuclear corrections.