We study the sensitivity of our recent MSTW 2008 NLO and NNLO PDF analyses to the values of the charm- and bottom-quark masses, and we provide additional public PDF sets for a wide range of these heavy-quark masses. We quantify the impact of varying m_c and m_b on the cross sections for W, Z and Higgs production at the Tevatron and the LHC. We generate 3- and 4-flavour versions of the (5-flavour) MSTW 2008 PDFs by evolving the input PDFs and alpha_S determined from fits in the 5-flavour scheme, including the eigenvector PDF sets necessary for calculation of PDF uncertainties. As an example of their use, we study the difference in the Z total cross sections at the Tevatron and LHC in the 4- and 5-flavour schemes. Significant differences are found, illustrating the need to resum large logarithms in Q^2/m_b^2 by using the 5-flavour scheme. The 4-flavour scheme is still necessary, however, if cuts are imposed on associated (massive) b-quarks, as is the case for the experimental measurement of Z b bbar production and similar processes.
AT HERA heavy quarks may contribute up to 30% of the structure function $F_2$. The introduction of heavy quarks requires an extension of the DGLAP formalism. The effect of using different heavy flavour number schemes, and different approaches to the running of $α_s$, are compared using the ZEUS PDF fit formalism. The potential of including charm data in the fit is explored, using $D^*$ double differential cross-sections rather than the inclusive quantity $F_2^{c\bar{c}}$.
I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $α_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also con…
I consider the effect on partons distribution functions (PDFs) of changes in the theoretical procedure used in a PDF fit. I consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at most $x$ values, the gluon distribution becoming softer at high values of $x$ and larger at small $x$, and the coupling constant $α_S(M_Z^2)$ falling, particularly at NNLO. The fit quality also deteriorates.I also consider lowering the kinematic cut on $W^2$ for DIS data and i…
We generate fixed three- and four-light-flavour sets of partons using MRST2004 partons as input. We show that it is important to set n_f=3 in the strong coupling, as well as in the splitting and coefficient functions, in order to obtain a consistent set of fixed-flavour partons. We compare the description of data using partons in both variable- and fixed-flavour-number-schemes.
Evaluating parton density systematic uncertainties in Monte~Carlo event generator predictions has long been achieved by reweighting between the original and systematic PDFs for the initial state configurations of the individual simulated events. This weighting is now pre-emptively performed in many generators, providing convenient weight factors for PDF and scale systematics -- including for NLO calculations where counterterms make the weight calculation complex. This note attempts a pedagogical discussion and empirical study of the consequences of neglecting the effects of PDF variations on t…
Due to the large masses of the charm and bottom quarks, their production cross sections are calculable within the perturbative QCD. This makes the heavy-quark mesons important observables in high-energy collisions of protons and nuclei. However, the available calculations for heavy-flavored-meson hadroproduction have been somewhat problematic in reliably describing the cross sections across the full kinematic range from zero to very high $p_{\rm T}$. This has put some question marks on the robustness of LHC heavy-flavored-meson measurements in studying the partonic structure of the colliding h…
The calculations of $Z + b{\bar b}$ tagged jet production performed in the four- and five-flavour schemes allow for detailed comparison of the heavy flavour structure of collinear and transverse momentum dependent (TMD) parton distributions as well as for detailed investigations of heavy quarks radiated during the initial state parton shower cascade. We have determined the first set of collinear and TMD parton distributions in the four-flavour scheme with NLO DGLAP splitting functions within the Parton-Branching (PB) approach. The four- and five-flavour PB-TMD distributions were used to calcul…
Transverse and longitudinal electroweak gauge boson parton distribution functions (PDFs) are computed in terms of deep-inelastic scattering structure functions, following the recently developed method to determine the photon PDF. The calculation provides initial conditions at the electroweak scale for PDF evolution to higher energies. Numerical results for the $W^\pm$ and $Z$ transverse, longitudinal and polarized PDFs, as well as the $γZ$ transverse and polarized PDFs are presented.
We discuss the parton branching (PB) evolution equation for transverse momentum dependent (TMD) parton distribution functions (PDFs), especially we concentrate on the angular ordering constrain and its effect on the TMD distributions. We discuss application of the PB TMDs to precise prediction of Drell-Yan transverse momentum spectrum at LHC, stressing the role of angular ordering in the low transverse momentum region. We compare the PB implementation of the angular ordering condition with the Kimber-Martin-Ryskin-Watt (KMRW), both at the analytical and numerical level.
I consider variations in the definition of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions, both at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO). I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. At both NLO and NNLO I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the distributions when a new MSTW-type global fit to data is performed for each GM-VFNS. At NLO the par…
We report on an update of the next-to-next-to-leading order (NNLO) ABKM09 parton distributions functions. They are obtained with the use of the combined HERA collider Run I inclusive deep-inelastic scattering (DIS) data and the partial NNLO corrections to the heavy quark electro-production taken into account. The value of the strong couplig constant $α^{\rm NNLO}_{\rm s}(M_{\rm Z})=0.1147(12)$ is obtained. The standard candle cross sections for the Tevatron collider and the LHC estimated with the updated PDFs are provided.
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…
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 $x$ 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 ${\bar u}$ or ${\bar d}$ in the disconnected insertion. This allows lattice calculations of separate flavors in both the conn…
We previously investigated the compatibility of the $Kimber$-$Martin$-$Ryskin$ ($KMR$) $unintegrated$ parton distribution functions ($UPDF$) with the experimental data on the proton (longitudinal) structure functions ($PSF$ ($PLSF$)). Recently $Golec-Biernat$ and $Stasto$ ($GBS$) demonstrated that the differential version of $KMR$ prescription and the implementations of angular (strong) ordering ($AOC$ ($SOC$)) constraints, cause the negative-discontinuous $UPDF$ with the ordinary parton distribution functions ($PDF$) as the input, which leads to a sizable effect on the calculation of $PSF$. I…
An important limitation in current fits of parton distribution functions (PDFs) is that PDF uncertainties do not include any source of theoretical uncertainty. Here we present a general method for incorporating theoretical uncertainties into PDF fits, focussing in particular on perturbative missing higher order uncertainties (MHOUs). We consider two methods for estimating the effect of MHOUs on PDFs, both based on scale variations. Firstly, we present PDF fits based on theoretical predictions with varied scales, and use these to estimate the associated MHOUs. Secondly, we discuss the construct…
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…
Focusing on hadron scattering at large partonic momentum fractions $x$, we compare nonperturbative QCD predictions for the asymptotic behavior of DIS structure functions and parton distribution functions (PDFs) to the $x$ and $Q$ dependence of phenomenological PDFs. In the CT18 NNLO global QCD analysis, higher-order radiative contributions and functional mimicry of PDF parametrizations result in about one unit of uncertainty in the effective powers of $(1-x)$ falloff of nucleon PDFs. Similar uncertainties are present in the case of the pion PDF, an object of growing interest in phenomenology.
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.
Parton distribution functions (pdfs) are an important ingredient for LHC phenomenology. Recent progress in determining pdfs from global analyses is reviewed, and some of the most important outstanding issues are highlighted. Particular attention is paid to the precision with which predictions for LHC `standard-candle' cross sections can be made, and also to new information that LHC can provide on pdfs.
We show how the photon input parton distribution function (PDF) may be calculated with good accuracy, and used in an extended DGLAP global parton analysis in which the photon is treated as an additional point-like parton. The uncertainty of the input photon PDF is relatively small, since the major part of the distribution (which is produced by the coherent emission of the photon from a proton that remains intact) is well known. We present the expected photon PDFs, and compare the predictions with ZEUS data for isolated photon electroproduction at negative rapidities.
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.
The flow of information in high-energy collisions has been recently investigated by various groups: this includes the entanglement entropy of the proton becoming classical information entropy of pdfs, jet splitting affecting entropy, or the entropy distribution in hadron decays. Here we examine fragmentation functions in this context, including their entropy as probability distributions, and propose it as one convenient number to characterize progress in their extraction. We also use the Kullback-Leibler divergence to examine relations between FFs and pdfs such as that of Barone, Drago and Ma.
I review the current status of global analysis of nuclear parton distributions and discuss some near-future prospects. I also advocate proton-nucleus (p-$A$) measurements at the LHC with $A\ll 208$ from the viewpoint of nuclear parton distributions.
We explicitly demonstrate how to correctly define the hadronic parton distributions (PDFs, TMDs, and GPDs) in the soft-wall AdS/QCD approach, based on the use of a quadratic dilaton field, providing confinement and spontaneous breaking of conformal and chiral symmetries. The power behavior of parton distributions at large values of the light-cone variable is consistent with quark counting rules and Drell-Yan-West duality. All parton distributions are defined in terms of profile functions, which depend on the light-cone coordinate and are fixed from PDFs and electromagnetic form factors.
Heavy quark parton distribution functions (PDFs) play an important role in several Standard Model and New Physics processes. Most PDF analyses rely on the assumption that the charm and bottom PDFs are generated perturbatively by gluon splitting and do not include any non-perturbative degrees of freedom. However, a non-perturbative, intrinsic heavy quark PDFs have been predicted in the literature. We demonstrate that to a very good approximation the scale-evolution of the intrinsic heavy quark content of the nucleon is governed by non-singlet evolution equations, and use this approximation to m…
We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton d…
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 approa…
Motivated by the possibility that it may be misleading to assume SU(3) symmetry in the analysis of hyperon β-decays, we study the sensitivity of the polarized parton densities, derived from the world data on inclusive polarized deep inelastic lepton-nucleon scattering, to variation of the value of the nonsinglet axial charge a_8 from its SU(3) value of 3F-D.
We derive relations between transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDFs f_1(x) and g_1(x) as input we predict the x- and pT-dependence of all twist-2 T-even TMDs.
We present preliminary results on the determination of spin-dependent, or polarised, Parton Distribution Functions (PDFs) from all relevant inclusive polarised DIS data. The analysis is performed within the NNPDF approach, which provides a faithful and statistically sound representation of PDFs and their uncertainties. We describe how the NNPDF methodology has been extended to the polarised case, and compare our results with other recent polarised parton sets. We show that polarised PDF uncertainties can be sizeably underestimated in standard determinations, most notably for the gluon.
We present the first official release of the nCTEQ nuclear parton distribution functions (nPDFs) with errors. The main addition to the previous nCTEQ PDFs is the introduction of PDF uncertainties based on the Hessian method. Another important improvement is the inclusion of pion production data from RHIC giving us a handle to constrain gluon PDF. In this presentation we briefly discuss the framework of our analysis and concentrate on the comparison of our results with those of other groups.
The impact of measurements of heavy-flavour production in deep inelastic $ep$ scattering and in $pp$ collisions on parton distribution functions is studied in a QCD analysis at next-to-leading order. Recent combined results of inclusive and heavy-flavour production cross sections in deep inelastic scattering at HERA are investigated together with heavy-flavour production measurements at the LHC. Differential cross sections of charm- and beauty-hadron production measured by the LHCb collaboration at the centre-of-mass energies of 5, 7 and 13 TeV as well as the recent measurements of the ALICE e…
Recent measurements of top quark pair production cross section, which is performed at the LHC and the Tevatron collider, are studied using Hessian profiling technique to obtain their impact on the parton distribution functions (PDFs). The top quark production data covers different center-of-mass energies $\sqrt{s}$= 1.96, 5.02, 7, 8 and 13 TeV in either $pp$ or $p\bar{p}$ collisions. It is explained how the Hessian profiling method may be used to assess the impact of these new data on PDFs and consequently on their predictions. In this research, the impact of recent measurements of top quark p…
We present the nCTEQ15 global analysis of nuclear parton distribution functions (nPDFs). The main addition to the previous nCTEQ PDFs is the introduction of PDF uncertainties based on the Hessian method. Another important improvement is the inclusion of pion production data from RHIC giving us a handle to constrain gluon PDF. In this presentation we briefly discuss the framework of our analysis and concentrate on the comparison of our results with those of other groups. Additionally we show a first estimate of the impact of the LHC pPb W/Z boson production data on the presented nCTEQ15 PDFs.
We provide a discussion of the impact of a subset of Drell-Yan data from LHC on the determination of the photon parton distribution function (PDF), using the NNPDF methodology. In previous work we have shown that the photon PDF determined from deep-inelastic scattering (DIS) data only has large uncertainties, suggesting the need for more data from other processes such as Drell-Yan, which unlike DIS, includes photon-induced contributions at leading order in QED. We describe the inclusion of ATLAS Drell-Yan W, Z data, which is a subset of the LHC data used in a final photon PDF determination, by…
We summarize recent results on i) the use of u-pdf's in the Monte-Carlo simulation of hadronic final states at high-energy colliders, and ii) attempts to characterize u-pdf's with precision in terms of nonlocal operator matrix elements.
The precise knowledge of parton distribution functions (PDFs) is indispensable to the accurate calculation of hadron-initiated QCD hard scattering observables. Much of our information on PDFs is extracted by comparing deep inelastic scattering (DIS) and lepton pair production (LPP) data to convolutions of the PDFs with the partonic cross sections of these processes. It is known that partonic cross sections receive large corrections in regions of phase space near partonic thresholds that can be resummed using threshold resummation techniques. The effect of threshold resummation on DIS and LPP d…
A new and simple statistical approach is performed to calculate the parton distribution functions (PDFs) of the nucleon in terms of light-front kinematic variables. Analytic expressions of x-dependent PDFs are obtained in the whole x region. And thereafter, we treat the temperature T as a parameter of the atomic number A to explain the nuclear EMC effect in the region $x \in [0.2, 0.7]$. We give the predictions of PDF ratios, and they are very different from those by other models, thus experiments aiming at measuring PDF ratios are suggested to provide a discrimination of different models.
This article gives an introduction to transverse momentum dependent (TMD) parton distribution functions and their use in shower Monte Carlo event generators for high-energy hadron collisions, and describes recent progress in the treatment of sea quark effects within a TMD parton-shower framework.
We study the potential of the LHCb 13 TeV single $W^{\pm}$ 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 fb$^{-1}$ and 300 fb$^{-1}$, to reducing the PDF uncertainty bands of the CT14HERA2 PDFs, using the error PDF updating package {\sc ePump}. The sensitivities of various experimental observables are compared. Generally, sizable reductions in PDF uncertainties can be observed in the 300 fb$^{-1}$ data sample, particularly in th…
The formulas directly connecting parton distribution functions (PDFs) and fragmentation functions (FFs) at the next to leading order (NLO) QCD with the same quantities at the leading order (LO) are derived. These formulas are universal, i.e. have the same form for all kinds of PDFs and FFs, differing only in the respective splitting functions entering there.
We suggest a classification scheme for parton distribution models, clarify the geometrical origin of unintegrated parton distribution relations, which were observed in various models, present new model relations, and provide for a so-called "spherical" model the analogous constraints for generalized parton distributions. Our findings suggest that various classes of uPDF and GPD models can be obtained from effective two-body light-cone wave functions.
We present a study of the interplay between PDF and EFT effects in high-mass Drell-Yan at the LHC. We quantify the impact of a consistent joint determination of the PDFs and Wilson coefficients on the bounds obtained on the EFT and examine the effect on the PDFs, determining the extent to which EFT signals could be reabsorbed into the large-$x$ quark and anti-quark PDFs. Finally, we present dedicated projections for the High-Luminosity LHC and evaluate its ultimate potential to constrain the EFT parameters, while taking into account potential modifications of the proton structure.
We employ models from effective two-body light-cone wave functions (LCWFs) to provide a link between generalized parton distributions (GPDs) and unintegrated parton distribution functions (uPDFs). Since we utilize the underlying Lorentz symmetry, GPDs can be entirely obtained from the parton number conserved LCWF overlaps. This also allows us to derive model constraints among GPDs. We illustrate that transversity distributions may be rather sizeable.
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…
The relations between TMDs and PDFs are obtained from the symmetry requirement: relativistic covariance combined with rotationally symmetric parton motion in the nucleon rest frame. This requirement is applied in the covariant parton model. Using the usual PDFs as an input, we are obtaining predictions for some polarized and unpolarized TMDs.
We investigate a possible use of direct photon production in association with a heavy quark in $pA$ collisions at the large hadron collider to constrain the nuclear gluon parton distribution function. This process is sensitive to both, the nuclear heavy quark and gluon parton distribution functions and is a very promising candidate to help determine the gluon nuclear PDF which is still largely untested.
We discuss how the operator product expansion (OPE) can be used to derive asymptotic expressions for certain integrals. This yields operator matrix elements (OME's) which determine the matching conditions for $\bar{\rm MS}$ parton densities across heavy flavour thresholds. Then we construct four and five-flavour densities from a three-flavour set via the AP equation using LO and NLO splitting functions.
The parton distributions functions (PDFs) derived from the NNLO QCD analysis of existing light-targets deep-inelastic-scattering data are presented. The NLO and NNLO PDFs are compared in order to analyze perturbative stability of the analysis and estimate impact of the higher-order QCD corrections. The main theoretical uncertainties and experimental uncertainties in PDFs due to all sources of experimental errors in data are estimated and used to assess corresponding uncertainties in the cross sections of other hadronic processes.
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 lar…
The LHC has recently released precise measurements of the transverse momentum distribution of the Z-boson that provide a unique constraint on the structure of the proton. Theoretical developments now allow the prediction of these observables through next-to-next-to-leading order (NNLO) in perturbative QCD. In this work we study the impact of incorporating these latest advances into a determination of parton distribution functions (PDFs) through NNLO including the recent ATLAS and CMS 7 TeV and 8 TeV $p_T^Z$ data. We investigate the consistency of these measurements in a global fit to the avail…
In this contribution we briefly report on the progress and open problems in parton distribution functions (PDFs), with emphasis on their implications for LHC phenomenology. Then we study the impact of the recent ATLAS and CMS W lepton asymmetry data on the NNPDF2.1 parton distributions. We show that these data provide the first constrains on PDFs from LHC measurements.
We present a study of the results obtained combining LO partonic matrix elements with either LO or NLO partons distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have flaws, sometimes serious, for some processes, so a modified optimal LO set is suggested. We investigate a wide variety of process, and the LO* pdf wor…
