Parton Distribution Functions Uncertainties Research Articles

Top-quark pole mass extraction at NNLO accuracy, from total, single- and double-differential cross sections for tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} + X production at the LHC

We extract the top-quark mass value in the on-shell renormalization scheme from the comparison of theoretical predictions for pp → tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} + 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 1σ uncertainty, whereas some datasets related to tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} 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 αs(MZ) and the top-quark mass, using the currently most precise experimental data on tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} + X total and multi-differential cross sections from the LHC.

Constraining the top-quark mass within the global MSHT PDF fit

We examine the ability of experimental measurements of top-quark pair production to constrain both the top-quark mass and the strong coupling within the global MSHT parton distribution function (PDF) fit. Specifically, we consider ATLAS and CMS measurements of differential distributions taken at a centre-of-mass energy of 8 TeV, as well as tbar{t} total cross section data taken at a variety of experiments, and compare to theoretical predictions including next-to-next-to-leading order corrections. We find that supplementing the global fit with this additional information results in relatively strong constraints on the top-quark mass, and is also able to bound the strong coupling in a limited fashion. Our final result is m_t=173.0pm 0.6~textrm{GeV} and is compatible with the world average pole mass extracted from cross section measurements of 172.5pm 0.7~textrm{GeV} by the Particle Data Group. We also study the effect of different top-quark masses on the gluon parton distribution function, finding changes at high x which nonetheless lie within the large PDF uncertainties in this region.

Parton distributions with scale uncertainties: a Monte Carlo sampling approach

We present the MCscales approach for incorporating scale uncertainties in parton distribution functions (PDFs). The new methodology builds on the Monte Carlo sampling for propagating experimental uncertainties into the PDF space that underlies the NNPDF approach, but it extends it to the space of factorisation and renomalisation scales. A prior probability is assigned to each scale combinations set in the theoretical predictions used to obtain each PDF replica in the Monte Carlo ensemble and a posterior probability is obtained by selecting replicas that satisfy fit-quality criteria. Our approach allows one to exactly match the scale variations in the PDFs with those in the computation of the partonic cross sections, thus accounting for the full correlations between the two. We illustrate the opportunities for phenomenological exploration made possible by our methodology for a variety of LHC observables. Sets of PDFs enriched with scale information are provided, along with a set of tools to use them.

Parton distributions need representative sampling

In global QCD fits of parton distribution functions (PDFs), a large part of the estimated uncertainty on the PDFs originates from the choices of parametric functional forms and fitting methodology. We argue that these types of uncertainties can be underestimated with common PDF ensembles in high-stake measurements at the Large Hadron Collider and Tevatron. A fruitful approach to quantify these uncertainties is to view them as arising from sampling of allowed PDF solutions in a multidimensional parametric space. This approach applies powerful insights gained in recent statistical studies of large-scale population surveys and quasi-Monte Carlo integration methods. In particular, PDF fits may be affected by the big data paradox, which stipulates that more experimental data do not automatically raise the accuracy of PDFs---close attention to the data quality and sampling of possible PDF solutions is as essential. To test if the sampling of the PDF uncertainty of an experimental observable is truly representative of all acceptable solutions, we introduce a technique (``a hopscotch scan'') based on a combination of parameter scans and stochastic sampling. With this technique, we examine the PDF uncertainty on key LHC cross sections at 13 TeV obtained with the public NNPDF4.0 fitting code, while accounting for the likelihood distribution. We show that the uncertainties on the charm distribution at a large momentum fraction $x$ and gluon PDF at small $x$ are enlarged. In PDF ensembles obtained in the analytic minimization (Hessian) formalism, the tolerance on the PDF uncertainty must be based on sufficiently complete sampling of PDF functional forms and choices of the experiments.

Parton distribution functions and QCD coupling constant from LHC and non-LHC data

We present a new QCD analysis of parton distribution functions (PDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). In the present paper, the role of special types of experimental measurements for extracting PDFs is investigated, and simultaneously the values of the strong coupling constant are determined. Essential elements of this QCD analysis are the HERA combined data as a base, heavy-quark cross-section measurement together with Tevatron data on jet production and H1 and ZEUS jet cross sections as ``non-LHC'' data, and especially the ``LHC'' dataset for top-quark and jet cross sections. These different datasets have allowed detailed information at low $x$, providing worthwhile information on the nucleon's flavor, and have played an important role for some PDFs at large-$x$ and strong coupling constant. Since the large-$x$ gluon PDF benefits from an accurate determination of quark PDFs, we have enough motivation to focus on the top-quark production and jet cross-section measurements from LHC to find the impact of these data on the gluon PDF and strong coupling constant. These experimental data have an impact on the relative uncertainties of PDF. The gluon PDF at large $x$ and the values of ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})$ are affected significantly. Although the main motivation of this paper is to focus on the gluon PDF and its uncertainty at large-$x$, giving notice to heavy PDF behavior in this region is also very important. We study the intrinsic charm (IC) using the BHPS model together with our extracted extrinsic charm PDF at large $x$, which can be very worthwhile for future experiments at the LHC.

Machine learning of log-likelihood functions in global analysis of parton distributions

Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In conventional analysis the Hessian approximation has been widely used for the estimation of the PDF uncertainties. The Lagrange Multiplier (LM) scan while being a more faithful method is less used due to computational limitations, and is the main focus of this study. We propose to use Neural Networks (NNs) and machine learning techniques to model the profile of the log-likelihood functions or cross sections for multi-dimensional parameter space in order to overcome those limitations which work beyond the quadratic approximations and meanwhile ensures efficient scans of the full parameter space. We demonstrate the efficiency of the new approach in the framework of the CT18 global analysis of PDFs by constructing NNs for various target functions, and performing LM scans on PDFs and cross sections at hadron colliders. We further study the impact of the NOMAD dimuon data on constraining PDFs with the new approach, and find enhanced strange-quark distributions and reduced PDF uncertainties. Moreover, we show how the approach can be used to constrain new physics beyond the Standard Model (BSM) by a joint fit of both PDFs and Wilson coefficients of operators in the SM effective field theory.

Complementarity of Lepton-Charge and Forward-Backward Drell-Yan Asymmetries for Precision Electroweak Measurements and Quark Density Determinations

We address the impact of future measurements of charged and neutral current Drell-Yan (DY) asymmetries and their combination on Parton Distribution Functions (PDFs) uncertainties. We quantify the reduction of PDF uncertainties using the QCD tool xFitter. We examine the effects of such reduced PDF errors on both Standard Model (SM) and Beyond SM (BSM) observables.

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.

EPPS21: a global QCD analysis of nuclear PDFs

We present an updated global analysis of collinearly factorized nuclear parton distribution functions (PDFs) at next-to-leading order in perturbative QCD. In comparison to our previous fit, EPPS16, the present analysis includes more data from proton-lead collisions at the Large Hadron Collider: 5 TeV double-differential CMS dijet and LHCb D-meson data, as well as 8 TeV CMS W^pm data. These new data lead to significantly better-constrained gluon distributions at small and intermediate values of the momentum fraction x, confirming the presence of shadowing and antishadowing for gluons in large nuclei. In addition, we include Jefferson Lab measurements of deeply inelastic scattering which probe nuclear PDFs at large x and low virtualities. For the first time within the Hessian framework, we now also explore the uncertainties of nuclear PDFs due to the errors in the baseline proton PDFs. We release the results of our analysis as a new public parametrization of nuclear PDFs called EPPS21.

Proton-PDF uncertainties in extracting nuclear PDFs from W^pm production in p+Pb collisions

We discuss the recent CMS Collaboration measurement of W^pm boson production in p+Pb collisions at 8.16 TeV in terms of the constraining power on nuclear parton distribution functions (PDFs). The impact of the free-proton PDF uncertainties on the nuclear PDF extraction is quantified by using a theoretical covariance-matrix method and Hessian PDF reweighting. We discuss different ways to mitigate these theoretical uncertainties, including self-normalization, forward-to-backward ratios and nuclear-modification ratios. It is found that none of these methods offer perfect cancellation of the free-proton PDFs but, with the present data uncertainties, the residual free-proton-PDF dependence has, conveniently for the global analyses, little effect on the extraction of the nuclear modifications. Based on a simple estimate of obtainable statistics at the LHC Run 3, we argue that this will change in the near future and it becomes more important to propagate the proton-PDF uncertainties accordingly. Using the obtained information on the correlations of the free-proton uncertainties, we also identify a new charge asymmetry ratio, where the cancellation of the proton-PDF uncertainties is found to be extremely good.

Light-nuclei gluons from dijet production in proton-oxygen collisions

The prospects of measuring a single-differential dijet cross section during the proposed short proton-oxygen data taking at LHC Run 3 are studied using next-to-leading-order perturbative QCD predictions. With reasonable experimental cuts and luminosity estimates, such a measurement is found to be feasible, and a few inverse nanobarns of integrated luminosity is estimated to be enough to yield new constraints on parton distribution functions (PDFs) of light nuclei. In the absence of a dedicated proton-proton reference, a mixed-energy nuclear modification ratio is proposed for canceling free-proton PDF uncertainties to obtain a direct access to the nuclear modifications of the parton distributions in oxygen.

Enhancing the Large Hadron Collider sensitivity to charged and neutral broad resonances of new gauge sectors

In scenarios beyond the Standard Model (BSM) characterised by charged (W′) or neutral (Z′) massive gauge bosons with large width, resonant mass searches are not very effective, so that one has to exploit the tails of the mass distributions measured at the Large Hadron Collider (LHC). In this case, the LHC sensitivity to new physics signals is influenced significantly by systematic uncertainties associated with the Parton Distribution Functions (PDF), particularly in the valence quark sector relevant for the multi-TeV mass region. As a BSM framework featuring such conditions, we consider the 4-Dimensional Composite Higgs Model (4DCHM), in which multiple W′ and Z′ broad resonances are present, with strongly correlated properties. By using the QCD tool xFitter, we study the implications on W′ and Z′ searches in Drell-Yan (DY) lepton decay channels that follow from the reduction of PDF uncertainties obtained through combining high-statistics precision measurements of DY lepton-charge and forward-backward asymmetries. We find that the sensitivity to the BSM states is greatly increased with respect to the case of base PDF sets, thereby enabling one to set more stringent limits on (or indeed discover) such new particles, both independently and in correlated searches.

Correlation of theoretical uncertainties in PDF fits and theoretical uncertainties in predictions

We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit calculations, both analytical and numerical, that these correlations can lead to corrections to the central values of the predictions, and reductions in both the PDF uncertainties and the theoretical uncertainties in the prediction. We illustrate our results with predictions for top production rapidity distributions and the Higgs total cross-section at the LHC, using the NLO NNPDF3.1 PDF set which incorporates missing higher order uncertainties. We conclude that the inclusion of correlations can increase both the accuracy and precision of predictions involving PDFs, particularly for processes with data already included in the PDF fit.

High-energy EFT probes with fully differential Drell-Yan measurements

We study the potential of fully-differential measurements of high-energy dilepton cross-sections at the LHC to probe heavy new physics encapsulated in dimension-6 interaction operators. The assessment is performed in the seven-dimensional parameter space of operators that induce energy-growing corrections to the Standard Model partonic cross-sections at the interference level, and in the two-dimensional subspace associated with the W and Y parameters. A considerable sensitivity improvement is found relative to single-differential measurements, owing to the possibility of probing at the interference level more directions in the seven-dimensional parameter space. The reduction of parton distribution function uncertainties in the fully-differential fit is also found to play a significant role. The results are interpreted in the minimal Z′ new-physics model, providing a concrete illustration of the advantages of the fully-differential analysis. We find that high-energy dilepton measurements can extend the Z′ exclusion and discovery potential well beyond the reach of direct searches in a large region of the parameter space.

Deuterium scattering experiments in CTEQ global QCD analyses: a comparative investigation

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 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 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.

Lepton-charge and forward-backward asymmetries in Drell-Yan processes for precision electroweak measurements and new physics searches

Precision determinations of Standard Model (SM) Electro-Weak (EW) parameters at the Large Hadron Collider (LHC) are dominated by uncertainties due to Parton Distribution Functions (PDFs). Reweighting and profiling techniques are routinely employed to treat this. We explore approaches based on combining measurements of charged current and neutral current Drell-Yan (DY) asymmetries to improve PDF uncertainties. We present the results of a numerical analysis performed with the open-source platform xFitter. PDF uncertainties are examined for lepton-charge and forward-backward asymmetries in regions of transverse and invariant masses near the vector-boson peak, based on LHC Run III and HL-LHC luminosity scenarios. We discuss the complementarity of the asymmetries in reducing PDF uncertainties in observables relevant to both SM and Beyond the SM (BSM) physics.

Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment * *Supported by the National Natural Science Foundation of China (11721505, 11875245) and the U.S. National Science Foundation (PHY-2013791)

We investigate the parton distribution function (PDF) uncertainty in the measurement of the effective weak mixing angle at the CERN Large Hadron Collider (LHC). The PDF-induced uncertainty is large in proton-proton collisions at the LHC due to the dilution effect. The measurement of the Drell-Yan forward-backward asymmetry ( ) at the LHC can be used to reduce the PDF uncertainty in the measurement. However, when including the full mass range of lepton pairs in the data analysis, the correlation between the PDF updating procedure and the extraction leads to a sizable bias in the obtained value. From our studies, we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the Z-pole region, while most of the sensitivity in reducing the PDF uncertainty remains. Furthermore, the lepton charge asymmetry in the W boson events as a function of the rapidity of the charged leptons, , is known to be another observable which can be used to reduce the PDF uncertainty in the measurement. The constraint from is complementary to that from , and thus no bias affects the extraction. The studies are performed using the error PDF Updating Method Package (ePump), which is based on Hessian updating methods. In this article, the CT14HERA2 PDF set is used as an example.

Impact of dijet and D-meson data from 5.02 TeV p+Pb collisions on nuclear PDFs

We discuss the new constraints on gluon parton distribution function (PDF) in lead nucleus, derivable with the Hessian PDF reweighting method from the 5.02 TeV p+Pb measurements of dijet (CMS) and D0-meson (LHCb) nuclear modification ratios. The impact is found to be significant, placing stringent constraints in the mid- and previously unconstrained small-x regions. The CMS dijet data confirm the existence of gluon anti-shadowing and the onset of small-x shadowing, as well as reduce the gluon PDF uncertainties in the larger-x region. The gluon constraints from the LHCb D0 data, reaching down to x ∼ 10−5 and derived in a NLO perturbative QCD approach, provide a remarkable reduction of the small-x uncertainties with a strong direct evidence of gluon shadowing. Furthermore, we find a good description of the data even down to zero D0-meson transverse momentum within a purely DGLAP-based approach without a need for imposing any non-linear effects. Importantly, the constraints obtained from the dijet and D0 data are mutually fully consistent, supporting the universality of nuclear PDFs in hard-scattering processes.

Impact of LHCb 13 TeV W and Z pseudo-data on the parton distribution functions * *Supported by the National Natural Science Foundation of China (11875142, 11965020) and the U.S. National Science Foundation (PHY-2013791. C.-P)

We study the potential of the LHCb 13 TeV single W ± and Z boson pseudo-data for constraining the parton distribution functions (PDFs) of the proton. As an example, we demonstrate the sensitivity of the LHCb 13 TeV data, collected with integrated luminosities of 5 and 300 , to reducing the PDF uncertainty bands of the CT14HERA2 PDFs, using the error PDF updating package EPUMP. The sensitivities of various experimental observables are compared. Generally, sizable reductions in PDF uncertainties can be observed in the 300 data sample, particularly in the small-x region. The double-differential cross section measurement of Z boson p T and rapidity can greatly reduce the uncertainty bands of u and d quarks in almost the whole x range, as compared to various single observable measurements.

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.