Implications of CTEQ PDF analysis for collider observables
Pavel M. Nadolsky
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Contribution to the Proceedings of XVI International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2008), London, UK, 7-11 April 2008; 4 pages
In the context of a recent CTEQ6.6 global analysis, we review a new technique for studying correlated theoretical uncertainties in hadronic observables associated with imperfect knowledge of parton distribution functions (PDFs). The technique is based on the computation of correlations between the predicted values of physical observables in the Hessian matrix method. It can be used, for example, to link the dominant PDF uncertainty in a hadronic cross section to PDFs for individual parton flavors at well-defined $(x,μ)$ values. As an illustration, we apply the PDF correlation analysis to study regularities in the PDF dependence of Z, W, and Higgs boson production cross sections at the Tevatron and LHC.
Recent developments in the CTEQ-TEA global QCD analysis are presented. The parton distribution functions CT10-NNLO are described, constructed by comparing data from many experiments to NNLO approximations of QCD.
We discuss recent CTEQ-TEA group activities after the publication of the CT18 global analysis of parton distribution functions (PDFs) in the proton. In particular, we discuss a new calculation for the photon content in the proton, termed as CT18lux and CT18qed PDFs, and the impact of novel charm- and bottom-quark production cross section measurements at HERA on the CT18 global analysis.
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 comparat…
We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strength $α_{s}(M_{Z})$. We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF fitting, and fully reproduces the correlated dependence of theoretical cross sections on $α_s$ and PDF parameters. This method is based on a statistical relation that allows one to add the uncertainty produced by $α_s$, computed with some special PDF sets, in quadrature with the PDF uncertainty obtained for the fixed $α_s$ value (such as the CTEQ6.6 PDF set). A serie…
We discuss an NNLO realization of the general mass scheme S-ACOT-$χ$ for treatment of heavy-flavour production in neutral current deep-inelastic scattering. Practical implementation of the NNLO calculation is illustrated on the example of semi-inclusive structure functions $F_{2 c}(x,Q)$ and $F_{L c}(x,Q)$.
Detailed studies have been carried out on the impact of the LHC top quark pair production data on gluon PDF, in the context of the CTEQ-TEA global PDF fit, with the ePump-updating method. The considered $t\bar{t}$ data include single differential distributions from ATLAS and double differential distributions from CMS, both at 8 TeV. All analyses have been carried out at the NNLO, using fastNNLO tables. We show that the sensitivity per data point of the LHC $t\bar{t}$ data is similar to that of jet data, as included in the CT14HERA2 fit, while the total sensitivity of the present $t\bar{t}$ dat…
We present the new CTEQ-TEA global analysis of quantum chromodynamics (QCD). In this analysis, parton distribution functions (PDFs) of the nucleon are determined within the Hessian method at the next-to-next-to-leading order (NNLO) in perturbative QCD, based on the most recent measurements from the Large Hadron Collider (LHC) and a variety of world collider data. Because of difficulties in fitting both the ATLAS 7 and 8 TeV $W$ and $Z$ vector boson production cross section data, we present four families of (N)NLO CTEQ-TEA PDFs, named CT18, A, X and Z PDFs, respectively. We study the impact of …
Kashi University（喀什大学）；Michigan State University（密歇根州立大学）；Xinjiang University（新疆大学）；Kennesaw State University（肯尼索州立大学）；Argonne National Laboratory（阿贡国家实验室）；Shanghai Jiao Tong University（上海交通大学）
An overview is given of recent progress on a variety of fronts in the global QCD analysis of the parton structure of the nucleon and its implication for collider phenomenology, carried out by various subgroups of the CTEQ collaboration.
We analyze the impact of the recent HERA run I+II combination of inclusive deep inelastic scattering cross-section data on the CT14 global analysis of PDFs. New PDFs at NLO and NNLO, called CT14$_{\textrm{HERA2}}$, are obtained by a refit of the CT14 data ensembles, in which the HERA run I combined measurements are replaced by the new HERA run I+II combination. The CT14 functional parametrization of PDFs is flexible enough to allow good descriptions of different flavor combinations, so we use the same parametrization for CT14$_{\textrm{HERA2}}$ but with an additional shape parameter for descri…
We study the global analysis for parton distributions as a function of the QCD strong coupling strength alpha_s, and present a new series of distributions that span the range 0.110 < alpha_s(m_Z) < 0.128. We use these distributions to explore the correlation between alpha_s and the gluon distribution; the viability of global analysis as a method to measure alpha_s; and the dependence on alpha_s of predictions for W, Z, inclusive jet, and Higgs boson production ($b \bar{b} \to H$ and $gg \to H$) cross sections at the Tevatron and the LHC. We find that the uncertainty in alpha_s is the dominant …
We overview progress in the development of general-purpose CTEQ PDFs. The preprint is based on four talks presented by H.-L. Lai and P. Nadolsky at the 17th International Workshop on Deep Inelastic Scattering and Related Subjects (DIS 2009).
We show for the first time preliminary results of nuclear parton distribution function analysis of charged lepton DIS and Drell-Yan data within the CTEQ framework including error PDFs. We compare our error estimates to estimates of different nPDF groups.
We present the new nCTEQ15 set of nuclear parton distribution functions with uncertainties. This fit extends the CTEQ proton PDFs to include the nuclear dependence using data on nuclei all the way up to 208^Pb. The uncertainties are determined using the Hessian method with an optimal rescaling of the eigenvectors to accurately represent the uncertainties for the chosen tolerance criteria. In addition to the Deep Inelastic Scattering (DIS) and Drell-Yan (DY) processes, we also include inclusive pion production data from RHIC to help constrain the nuclear gluon PDF. Furthermore, we investigate t…
By applying the Error PDF Updating Method, we analyze the impact of the absolute and normalized single differential cross-sections for top-quark pair production data from the ATLAS and CMS experiments at the Large Hadron Collider, at a centre-of-mass energy of $\sqrt{s}= 8$ TeV, on the CT14HERA2 PDFs. We find that the top quark pair single differential distributions provide minor constraints on the CT14HERA2 gluon PDF when the nominal CT14HERA2 inclusive jet production data are included in the fit. Larger constraints on the gluon distribution are present when the jet data are removed (CT14HERA…
We study the impact of the lattice data on the determination of the strangeness asymmetry distribution $s_-(x) \equiv s(x) - {\bar s}(x)$ in the general CTEQ-TEA global analysis of parton distribution functions (PDFs) of the proton. Firstly, we find that allowing a non-vanishing $s_-(x)$, at the initial $Q_0=1.3$ GeV scale, in a global PDF analysis leads to the quality of the CT18As fit similar to CT18A. Secondly, including the lattice data in the CT18As\_Lat fit greatly reduces the $s_-$-PDF error band size in the large $x$ region. To further reduce its error would require more precise lattic…
We present the new CTEQ-TEA global analysis of quantum chromodynamics (QCD). In this analysis, parton distribution functions (PDFs) of the nucleon are determined within the Hessian method at the next-to-next-to leading order (NNLO) in perturbative QCD, based on the most recent measurements from the Large Hadron Collider (LHC) and a variety of world collider data. Because of difficulties in fitting both the ATLAS 7 and 8 TeV $W$ and $Z$ vector boson production cross section data, we present two families of PDFs, named CT18 and CT18$Z$ PDFs, respectively, without and with the ATLAS 7 TeV $W$ and…
The possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon is investigated together with theoretical issues arising in its interpretation. Results from the global PDF analysis are presented. The separation of the universal component of the nonperturbative charm from the rest of the radiative contributions is discussed and the potential impact of a nonperturbative charm PDF on LHC scattering processes is illustrated. An estimate of nonperturbative charm magnitude in the CT14 and CT14HERA2 global QCD analyses at the next-to-next-to le…
The latest CTEQ6.6 parton distributions, obtained by global analysis of hard scattering data in the framework of general-mass perturbative QCD, are employed to study theoretical predictions and their uncertainties for significant processes at the Fermilab Tevatron and CERN Large Hadron Collider. The previously observed increase in predicted cross sections for the standard-candle W and Z boson production processes in the general-mass scheme (compared to those in the zero-mass scheme) is further investigated and quantified. A novel method to constrain PDF uncertainties in LHC observables, by eff…
We investigate the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon, theoretical issues arising in its interpretation, and its potential impact on LHC scattering processes. The "fitted charm" PDF obtained in various QCD analyses contains a process-dependent component that is partly traced to power-suppressed radiative contributions in DIS and is generally different at the LHC. We discuss separation of the universal component of the nonperturbative charm from the rest of the radiative contributions and estimate its magnitude in…
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…
A selection of the latest and most frequently used PDFs is incorporated in PYTHIA8, including the MC-adapted PDFs from the MSTW and CTEQ collaborations. This thesis examines the differences in PDFs as well as the effect they have on results of simulations. The results are also compared to data collected by the CDF experiment.
A selection of the latest and most frequently used parton distribution functions (PDFs) is incorporated in Pythia8, including the Monte Carlo-adapted PDFs from the MSTW and CTEQ collaborations. This article examines the differences in PDFs as well as the effect they have on results of simulations and compare with data collected by the CDF experiment. Monte Carlo-adapted PDFs do a better job than leading- and next-to-leading order PDFs for many observables, but there is room for further improvements.
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 data set, along with the data sets 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-$p_T$ $Z$ bosons, are included to achieve the greatest sensitivity to the PDFs. The parton distributions are determined at NLO and N…
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.…
We summarize several projects carried out by the CTEQ global analysis of parton distribution functions (PDFs) of the proton during 2010. We discuss a recently released CT10 family of PDFs with a fixed and variable QCD coupling strength; implementation of combined HERA and Tevatron lepton asymmetry data sets; theoretical issues associated with the analysis of $W$ charge asymmetry in PDF fits; PDFs for leading-order shower programs; and constraints on new color-octet fermions from the hadronic data.
We present predictions for relevant LHC observables obtained with the NNPDF2.0 set. We compute the combined PDFs uncertainties on these observables, and show that combining errors in quadrature yields an excellent approximation to exact error propagation. We then compare the NNPDF2.0 results to the other global PDF fits using a common value of $α_s$. At LHC 7 TeV, reasonable agreement, both in central values and in uncertainties, is found for NNPDF2.0, CTEQ6.6 and MSTW08.
Using the new schemes provided by the CTEQ and MRST collaborations and by Alekhin, we analyse the uncertainties due to the parton distribution functions (PDFs) on the next-to-leading-order cross sections of the four main production processes of the Standard Model Higgs boson at the LHC and the Tevatron. In the Higgs mass range where the production rates are large enough, the spread in the uncertainties when the three sets of PDFs are compared is of about 15% in all processes and at both colliders. However, within one given set of PDFs, the deviations from the values obtained with the reference…
A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a "meta-parametrization" based on a common functional form. By analyzing parameters of the meta-parametrizations from all input PDF ensembles, a combined PDF ensemble can be produced that has a smaller total number of PDF member sets than the original ensembles. The meta-parametrizations simplify the computation of the PDF uncertainty in theoretical predictio…
We have studied the production of single isolated prompt photons in high energy proton-proton collisions at the RHIC ($\sqrt{s}$= 200 GeV) and the LHC ($\sqrt{s}$= 7 TeV) energies within the frame work of perturbative QCD upto next-to leading order of strong coupling ($α_s$). We have used five different parameterizations of parton distribution function (PDF) starting from the old CTEQ4M to the new CT10 distributions and compared our results with the recent single prompt photon data from the PHENIX and the CMS collaborations. The prompt photon cross-section is found to be described equally well…
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 precisio…
We present updates to a recent CTEQ-Jefferson Lab (CJ) global analysis of parton distribution functions with a new set of electroweak data that provide unique access to quark flavor separation in the proton. In particular, recent $W$ and $Z$ boson measurements from the STAR experiment at RHIC put additional constraints on light quarks and antiquarks near the valence regime. The new measurement of the Drell-Yan lepton pair production ratio in $p+p$ and $p+d$ collisions by the SeaQuest experiment at Fermilab extends the large-$x$ coverage of the previous E866 experiment and sheds new light on th…
We discuss c\bar{c} and b\bar{b} pair productions at ep collider for studying extremely small x(g) region. It has been shown that Large Hadron electron Collider (LHeC) has a reach of about x(g)>10^{-6}. The aim of this work is to show that the PDF uncertainties in the heavy flavour production. Maximum difference of cross section between PDFs 60% has been found in the process of ep\rightarrow eq\bar{q}X.
We calculate cross-sections and cross-section ratios of a charm quark production in association with a $W$ gauge boson at next-to-leading order QCD using MadGraph and CT10NNLO, CT14NNLO, and MSTW2008NNLO PDFs. We compare the results with measurements from the CMS detector at the LHC at a center-of-mass energy of 7TeV. Moreover, we calculate absolute and normalized differential cross-sections as well as differential cross-section ratios as a function of the lepton pseudorapidity from the $W$ boson decay. The correlation between the CT14NNLO PDFs and predictions for $W+$ charm data are studied a…
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…
We discuss the effect of the Photon Initiated (PI) process on the dilepton channel at the LHC. Adopting various QED PDF sets, we evaluate the contribution produced by two resolved photons which is not included in the Equivalent Photon Approximation (EPA). We compare the PI central value as predicted by the CTEQ, MRST and NNPDF collaborations. With the NNPDF2.3QED set of replicas we also estimate the PDF uncertainties on the PI central value. We show the effect of the inclusion of the PI contribution and its PDF uncertainties on neutral heavy Z'-boson searches. We explore the two scenarios of n…
Parton Distribution Functions (PDFs) are essential non-perturbative inputs for calculation of any observable with hadronic initial states. These PDFs are released by individual groups as discrete grids as a function of the Bjorken-x and energy scale Q. The LHAPDF project at HepForge maintains a repository of PDFs from various groups in a new standardized LHAPDF6 format, as well as older formats such as the CTEQ PDS grid format. ManeParse is a package that provides PDFs within the Mathematica framework to facilitate calculating and plotting. The program is self-contained so there are no externa…
We present a systematic study of uncertainties due to parton distributions and the strong coupling on the gluon-fusion production cross section of the Standard Model Higgs at the Tevatron and LHC colliders. We compare procedures and results when three recent sets of PDFs are used, CTEQ6.6, MSTW08 and NNPDF1.2, and we discuss specifically the way PDF and strong coupling uncertainties are combined. We find that results obtained from different PDF sets are in reasonable agreement if a common value of the strong coupling is adopted. We show that the addition in quadrature of PDF and alphas uncerta…
We describe the implementation of Quantum Electrodynamic (QED) evolution at Leading Order (LO) along with Quantum Chromodynamic (QCD) evolution at Next-to-Leading Order (NLO) in the CTEQ-TEA Global analysis package. The inelastic contribution to the photon Parton Distribution Function (PDF) is described by a two-parameter ansatz, coming from radiation off the valence quarks, and based on the CT14 NLO PDFs. Setting the two parameters to be equal allows us to completely specify the inelastic photon PDF in terms of the inelastic momentum fraction carried by the photon, $p_0^γ$, at the initial sca…
We consider the impact of the recent data obtained by the LHC, Tevatron, and fixed-target experiments on the nucleon quark distributions with a particular focus on disentangling different quark species. An improved determination of the poorly known strange sea distribution is obtained due to including data from the neutrino-induced deep-inelastic scattering experiments NOMAD and CHORUS. The impact of the associated (W + c) production data by CMS and ATLAS on the strange sea determination is also studied and a comparison with earlier results based on the collider data is discussed. Finally, the…
We extract new parton distribution functions (PDFs) of the proton by global analysis of hard scattering data in the general-mass framework of perturbative quantum chromodynamics. Our analysis includes new theoretical developments together with the most recent collider data from deep-inelastic scattering, vector boson production, and single-inclusive jet production. Due to the difficulty in fitting both the DO Run-II W lepton asymmetry data and some fixed-target DIS data, we present two families of PDFs, CT10 and CT10W, without and with these high-luminosity W lepton asymmetry data included in …
A clear understanding of nuclear parton distribution functions (nPDFs) plays a crucial role in the interpretation of collider data taken at the Relativistic Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC) and in the near future at the Electron-Ion Collider (EIC). Even with the recent inclusions of vector boson and light meson production data, the uncertainty of the gluon PDF remains substantial and limits the interpretation of heavy ion collision data. To obtain new constraints on the nuclear gluon PDF, we extend our recent nCTEQ15WZ+SIH analysis to inclusive quarkonium and open hea…
The role of global QCD analysis of parton distribution functions (PDFs) in collider physics at the Tevatron and LHC is surveyed. Current status of PDF analyses are reviewed, emphasizing the uncertainties and the open issues. The stability of NLO QCD global analysis and its prediction on "standard candle" W/Z cross sections at hadron colliders are investigated. The importance of the precise measurement of various W/Z cross sections at the Tevatron in advancing our knowledge of PDFs, hence in enhancing the capabilities of making significant progress in W mass and top quark parameter measurements…
We review the current state of the art in the determination of the parton substructure of the nucleon, as expressed in terms of parton distribution functions (PDFs), and probed in high-energy lepton-hadron and hadron-hadron collisions, and we assess their implications for current precision collider phenomenology, in particular at the Large Hadron Collider (LHC). We review the theoretical foundations of PDF determination: the way cross sections are expressed in terms of PDFs using perturbative QCD factorization and evolution, the methodology used to extract PDFs from experimental data, and the …
