There are two types of polarizations in spin-1 hadrons, and they are vector and tensor polarizations. The latter is a unique one since it does not exist in the spin-1/2 proton. The vector-polarized PDFs are the same for both the proton and spin-1 hadrons; therefore, we mainly investigate the unique PDFs in tensor-polarized hadrons. By using the operator product expansion, the twist-3 PDF $f_{LT}$ can be expressed by two terms in the same way with $g_T$ of the proton. The first term is determined by the twist-2 PDF $f_{1LL}$ (or $b_1$) which was measured by an experiment, and the second term is expressed by twist-3 quark-gluon distributions. If we neglect the higher-twist effects, $f_{LT}$ is simply given by $f_{1LL}$, and this relation is similar to the Wandzura-Wilczek relation of $g_T$. Furthermore, a new sum rule is also obtained for $f_{2LT}=2/3 f_{LT}- f_{1LL}$, which is analogous to the Burkhardt-Cottingham sum rule, in the tensor-polarized spin-1 hadrons. In future, these interesting relations could be studied at accelerator facilities, such as the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility in Russia, the proposed electron-ion colliders in US and China.
We estimate the amount of collective "elliptic flow" expected at mid-rapidity in proton-proton (p-p) collisions at the CERN Large Hadron Collider (LHC), assuming that any possible azimuthal anisotropy of the produced hadrons with respect to the plane of the reaction follows the same overlap-eccentricity and particle-density scalings as found in high-energy heavy ion collisions. Using a Glauber eikonal model, we compute the p-p eccentricities, transverse areas and particle-multiplicities for various phenomenological parametrisations of the proton spatial density. For realistic proton transverse…
Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist 3 and twist 4 in addition to the twist-2 ones, so that full investigations became possible for structure functions of spin-1 hadrons in the same level with those of the spin-1/2 nucleons. Furthermore, twist-3 tensor-polarized multiparton distribution functions were also recently found for spin-1 hadrons. In this work, we show relations among the collinear pa…
After a brief recapitulation of the general interest of parton densities, we discuss multiple hard interactions and multiparton distributions. We report on recent theoretical progress in their QCD description, on outstanding conceptual problems and on possibilities to use multiparton distributions as a laboratory to test and improve our understanding of hadron structure.
Multiple parton interactions in relativistic heavy ion reactions result in transverse momentum diffusion and medium induced non-Abelian energy loss of the hard probes traversing cold and hot nuclear matter. A systematic study of the interplay of nuclear effects on the $p_T \geq 2$ GeV inclusive hadron spectra demonstrates that the competition between nuclear shadowing, multiple scattering and jet quenching leads to distinctly different enhancement/suppression of moderate and high-$p_T$ hadron production in $d+Au$ and $Au+Au$ collisions at RHIC. The associated increase of di-jet acoplanarity, m…
We investigate several ingredients for a theory of multiple hard scattering in hadron-hadron collisions. Issues discussed include the space-time structure of multiple interactions, their power behavior, spin and color correlations, interference terms, scale evolution and Sudakov logarithms. We discuss possibilities to constrain multiparton distributions by lattice calculations and by connecting them with generalized parton distributions. We show that the behavior of two-parton distributions at small interparton distances leads to problems with ultraviolet divergences and with double counting, …
We perform a detailed investigation of multiple hard interactions in hadron-hadron collisions. We discuss the space-time, spin and color structure of multiple interactions, classify different contributions according to their power behavior and provide several elements required for establishing all-order factorization. This also allows us to analyze the structure of Sudakov logarithms in double hard scattering. We show how multiparton distributions can be constrained by lattice calculations, by connecting them with generalized parton distributions, and by calculating their behavior at large tra…
We point out a problem of the phenomenological definition of the valence partons as the difference between the partons and antipartons in the context of the NNLO evolution equations. After demonstrating that the classification of the parton degrees of freedom (PDF) of the parton distribution functions (PDFs) are the same in the QCD path-intergral formulations of the hadronic tensor and the quasi-PDF with LaMET, we resolve the problem by showing that the proper definition of the valence should be in terms of those in the connected insertions only. We also prove that the strange partons appear a…
This paper presents a new event generator, ALPGEN, dedicated to the study of multiparton hard processes in hadronic collisions. The code performs, at the leading order in QCD and EW interactions, the calculation of the exact matrix elements for a large set of parton-level processes of interest in the study of the Tevatron and LHC data. The current version of the code describes the following final states: (W -> ffbar') QQbar+ N jets (Q being a heavy quark, and f=l,q), with N<=4; (Z/gamma* -> f fbar)+QQbar+Njets (f=l,nu), with N<=4; (W -> ffbar') + charm + N jets (f=l,q), N<= 5; (W -> f fbar') +…
We calculate the nuclear dependence of direct photon production in hadron-nucleus collisions. In terms of a multiple scattering picture, we factorize the cross section for direct photon production into calculable short-distance partonic parts times multiparton correlation functions in nuclei. We present the hadron-nucleus cross section as $A^α$ times the hadron-nucleon cross section. Using information on the multiparton correlation functions extracted from photon-nucleus experiments, we compute the value of $α$ as a function of transverse momentum of the direct photon. We also compare our resu…
Theoretical arguments, supported by other indirect evidence, suggest that the wave function of high-x partons should be narrower than that of low-x ones. In this article, we present a modification to the variable impact parameter framework of Pythia 8 to model this effect. In particular, a Gaussian hadronic matter profile is introduced, with a width dependent on the x value of the constituent being probed. Results are compared against the default single- and double-Gaussian profiles, as well as an intermediate overlap function.
Particle production mechanisms in proton+proton and heavy-ion collisions at the LHC energies are discussed. An attempt is made to connect p+p to heavy-ion collisions in understanding the final state observables. New emerging phenomena like Multipartonic Interactions (MPI) and Color Reconnection (CR) mechanism are important in understanding heavy-ion like behaviors in high-multiplicity p+p events. Particle spectra, Multipartonic Interactions, Strangeness enhancement, Nuclear modification factor etc. are few of the aspects, which are discussed in this presentation.
Sum rules for structure functions and their twist-2 relations have important roles in constraining their magnitudes and $x$ dependencies and in studying higher-twist effects. The Wandzura-Wilczek (WW) relation and the Burkhardt-Cottingham (BC) sum rule are such examples for the polarized structure functions $g_1$ and $g_2$. Recently, new twist-3 and twist-4 parton distribution functions were proposed for spin-1 hadrons, so that it became possible to investigate spin-1 structure functions including higher-twist ones. We show in this work that an analogous twist-2 relation and a sum rule exist f…
The next-to-leading order (NLO) evolution of the parton distribution functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive (integrated) PDFs and done using inclusive NLO kernels. We report here on the ongoing project, called KRKMC, in which NLO DGLAP evolution is performed for the exclusive multiparton (fully unintegrated) distributions (ePDFs) with the help of the exclusive kernels. These kernels are calculated within the two-parton phase space for the non-singlet evolution, using Cu…
We discuss the multiplicity distribution for highest accessible energies of $pp$- and $\bar pp$- interactions from the point of view of the multiparton collisions. The inelastic cross sections for the single, $σ_1$, and multiple (double and, presumably, triple, $σ_{2+3}$) parton collisions are extracted from the analysis of the experimental data on the multiplicity distribution up to the Tevatron energies. It follows that $σ_1$ becomes energy independent while $σ_{2+3}$ increases with $\sqrt{s}$ for $\sqrt{s}\ge$ 200 GeV. The observed growth of $<p_{\perp}>$ with multiplicity is attributed to …
We propose an analysis method for the leading-twist operator product expansion based lattice QCD determinations of the valence parton distribution function (PDF). In the first step, we determine the confidence-intervals of the leading-twist $\overline{\mathrm{MS}}$ Wilson coefficients, $C_n(μ^2 z^2)$, of the equal-time bilocal quark bilinear, given the lattice QCD matrix element of Ioffe-time distribution for a particular hadron $H$ as well as the prior knowledge of the valence PDF, $f(x,μ)$ of the hadron $H$ determined via global fit from the experimental data. In the next step, we apply the …
Following our previous proposal [1], we construct a class of good "lattice cross sections" (LCSs), from which we could study partonic structure of hadrons from ab initio lattice QCD calculations. These good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that proposed functions for la…
Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD calculations of good "lattice cross sections", which are basically single-hadron matrix elements that are lattice QCD calculable and perturbative QCD factorizable into the PDFs. To demonstrate the existence of good "lattice cross sections", we take quasi-quark distribution introduced by Ji [1] as a case study to show that it could be factorized into the PDFs to all ord…
Transverse single-spin asymmetries in inclusive deep inelastic lepton-nucleon scattering can be generated through multiphoton exchange between the leptonic and the hadronic part of the process. Here we consider the two-photon exchange, and mainly focus on the transverse target spin asymmetry. In particular, we investigate the case where two photons couple to different quarks. Such a contribution involves a quark-photon-quark correlator in the nucleon, which has a (model-dependent) relation to the Efremov-Teryaev-Qiu-Sterman quark-gluon-quark correlator T_F. Using different parametrizations for…
We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer ($Q^2 \sim 4\, {\rm GeV^2}$) to suppress t…
Recent high precision experimental data from a variety of hadronic processes opens new opportunities for determination of the collinear parton distribution functions (PDFs) of the proton. In fact, the wealth of information from experiments such as the Large Hadron Collider (LHC) and others, makes it difficult to quickly assess the impact on the PDFs, short of performing computationally expensive global fits. As an alternative, we explore new methods for quantifying the potential impact of experimental data on the extraction of proton PDFs. Our approach relies crucially on the correlation betwe…
The rates of multiparton collisions in high energy hadronic interactions provide information on the typical transverse distances between partons in the hadron structure. The different configurations of the hadron in transverse space are, on the other hand, at the origin of hadron diffraction. The relation between the two phenomena is exploted in an eikonal model of hadronic interactions.
A precise knowledge of nuclear parton distribution functions (nPDFs) is -- among other things -- important for the unambiguous interpretation of hard process data taken in pA and AA collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The available fixed target data for deep inelastic scattering (DIS) and Drell-Yan (DY) lepton pair production mainly constrain the light quark distributions. It is hence crucial to include more and more collider data in global analyses of nPDFs in order to better pin down the different parton flavors, in particular the glu…
Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross section data. We review definitions of the PDFs and their relations to high-energy cross sections. We focus on the PDFs in protons, but also discuss PDFs in nuclei. We review in some detail the standard statistical treatment needed to fit the PDFs to data using the Hessian method. We discuss tests that can be used to critically examine whether the assumptions are…
We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at $\mathcal O(α_s)$, both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presen…
The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the o…
We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot be uniquely determined solely based on discrete experimental measurements because of a mathematical property of mimicry of PDF parametrizations that we prove using a representation based on Bézier curves. Predictions of nonperturbative QCD approaches for the $x$ dependence of PDFs instead should be cast in a form that enables decisive comparisons against ex…
Recently the concept of quasi parton distributions (quasi-PDFs) for hadrons has been proposed. Quasi-PDFs are defined through spatial correlation functions and as such can be computed numerically using quantum chromodynamics on a four-dimensional lattice. As the hadron momentum is increased, the quasi-PDFs converge to the corresponding standard PDFs that appear in factorization theorems for many high-energy scattering processes. Here we investigate this new concept in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator mode…
Studying the structure of nucleons is not only important to understanding the strong interactions of quarks and gluons, but also to improving the precision of new-physics searches. Since a broad class of experiments, including the LHC and dark-matter detection, require Standard-Model backgrounds with parton distribution functions (PDFs) as inputs for disentangling SM contributions from potential new physics. For a long time, lattice calculations of the PDFs (as well as many hadron structures) has been limited to the first few moments. In this talk, we present a first direct calculation of the …
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 …
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization…
We derived the conditions on certain combinations of integrals of the fragmentation functions of pion using HERMES data of the sum for the charged pion multiplicities from semi-inclusive deep-inelastic scattering (SIDIS) off the deuteron target. In our derivation the nucleon parton distribution functions (PDFs) are assumed to be isospin SU(2) symmetric. Similar conditions have also been obtained for the fragmentation functions (FFs) of kaon by the sum of charged kaon multiplicities as well. We have chosen several FFs to study the impact of those conditions we have derived. Among those FFs, onl…
We explain a gluon transversity, transverse-momentum-dependent parton distribution functions (TMDs), and parton distribution functions (PDFs) for spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no direct contribution from the nucleons, it is an appropriate quantity to probe an exotic component in the spin-1 deuteron beyond a simple bound system of the nucleons. We show how the gluon transversity can be measured at hadron accelerator facilities by the Drell-Yan process in addition to lep…
The prospects for a measurement of nuclear parton distribution functions (PDFs) at the Large Hadron--Electron Collider are discussed in the light of recent progress made in the front of global analysis of nuclear PDFs.
Determinations of the proton's collinear parton distribution functions (PDFs) are emerging with growing precision due to increased experimental activity at facilities like the Large Hadron Collider. While this copious information is valuable, the speed at which it is released makes it difficult to quickly assess its impact on the PDFs, short of performing computationally expensive global fits. As an alternative, we explore new methods for quantifying the potential impact of experimental data on the extraction of proton PDFs. Our approach relies crucially on the Hessian correlation between theo…
The description of the internal structure of hadrons is one of the main goal of QCD. At moderate energy scales, the hadronic representation succeeds to the partonic description, rendering challenging the description of the dynamics of scattering processes and hadronic structure. The information on the hadron structure is embodied in the long distance contributions which are defined as Parton Distribution Functions (PDFs). PDFs are a key framework for connecting the low and high-energy regimes, in that the knowledge on non- perturbative QCD carries important consequences at the high-energy leve…
In this article, we review recent lattice calculations on the $x$-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of…
The nuclear parton distribution functions (nPDFs) of gluons are known to be difficult to determine with fits of deep inelastic scattering (DIS) and Drell-Yan (DY) data alone. Therefore, the nCTEQ15 analysis of nuclear PDFs added inclusive neutral pion production data from RHIC to help in constraining the gluon. In this analysis, we present a new global analysis of nuclear PDFs based on a much larger set of single inclusive light hadron data from RHIC and the LHC. Using our new nCTEQ code (nCTEQ++) with an optimized version of INCNLO we study systematically the limitations of the theory and the…
Transverse-momentum-dependent parton distribution functions (TMDs) were investigated at the twists 3 and 4 for spin-1 hadrons in addition to the twist-2 ones. They were found by studying all the possible decomposition of a quark correlation function in a Lorentz-invariant way with the Hermiticity and parity invariance. The time-reversal invariance was not imposed for the TMDs due to an active role of gauge links; however, they were used for collinear parton distribution functions (PDFs) by integrating the TMDs over the transverse momentum. We found that 30 TMDs exist in the tensor-polarized sp…
We study proton-(anti)proton collisions at the LHC or Tevatron in the presence of experimental restrictions on the hadronic final state and for generic parton momentum fractions. At the scale Q of the hard interaction, factorization does not yield standard parton distribution functions (PDFs) for the initial state. The measurement restricting the hadronic final state introduces a new scale μ_B << Q and probes the proton prior to the hard collision. This corresponds to evaluating the PDFs at the scale μ_B. After the proton is probed, the incoming hard parton is contained in an initial-state jet…
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 present for the first time complete next-to-next-to-leading-order coefficient functions to match flavor non-singlet quark correlation functions in position space, which are calculable in lattice QCD, to parton distribution functions (PDFs). Using PDFs extracted from experimental data and our calculated matching coefficients, we predict valence-quark correlation functions that can be confronted by lattice QCD calculations. The uncertainty of our predictions is greatly reduced with higher order matching coefficients. By performing Fourier transformation, we also obtain matching coefficients f…
We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia ($η_c$ and $η_b$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light-front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PD…
Vector meson production in ultra-peripheral pA and AA collisions at the CERN Large Hadron Collider (LHC) are very sensitive to Parton Distribution Functions (PDF) as well as to their leading-order, next-to-leading-order, and medium corrections. This process is a complimentary tool to explore the effects of different PDFs in particle production in proton-nucleus and nucleus-nucleus central collisions. Existing and forthcoming data available, e.g., from ALICE and CMS, may be used in conjunction with our theoretical predictions to constrain the PDFs. We make predictions for rapidity distributions…
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…
This perturbative Quantum Chromo Dynamics (pQCD) analysis attempts to present a simultaneous determination of parton distribution functions (PDFs) and the strong coupling $α_s(M^2_Z)$ from inclusion of inclusive H1 and ZEUS jet, DiJets and TriJets production cross sections data on the HERA I and II combined data, as the central data sets for probing the internal structure of proton. To present an accurate pQCD analysis, we separate the role and influence of inclusion jet production cross sections data from inclusion of the strong coupling $α_s(M^2_Z)$ as an extra fit parameter parameter on the…
I explain the current status of parton-distribution-function (PDF) studies and future experimental prospects on their determinations. First, unpolarized PDFs of the nucleon are introduced as a field of precision QCD physics including higher-order $α_s$ corrections. Second, nuclear PDFs and polarized nucleonic PDFs are discussed. Third, the determination of fragmentation functions is explained. Forth, the three-dimensional (3D) structure functions are discussed in connection with the origin of the nucleon spin and gravitational form factors of hadrons. By the 3D structure functions, gravitation…
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.
Studying the possible breaking of various parton model symmetries by the parton distribution functions of the nucleon can provide important information for the non-perturbative structure of hadrons and the strong interaction. We review theoretical calculations for the breaking of flavor symmetry, quark-antiquark symmetry and charge symmetry in the unpolarized and polarized nucleons using the meson cloud model. We report an estimation for the total distribution of strange and antistrange quarks in the nucleon by combining theoretical calculations of SU(3) flavor symmetry breaking with light ant…
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolati…
Generalizing the Soffer Bound: Positivity Constraints on Parton Distributions of Spin-3/2 Particles
Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Quark Matter Research Center, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子研究中心）；KEK Theory Center, Institute of Particle and Nuclear Studies, KEK（日本高能加速器研究机构粒子与核研究部KEK理论中心）；Heavy Ion Science and Technology Key Laboratory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所重离子科学与技术重点实验室）；School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We show that measurements of the forward-backward charge asymmetry ($A_{FB}(M,y)$) of Drell-Yan dilepton events produced at hadron colliders provide a new powerful tool to constrain Parton Distribution Functions (PDFs). PDF uncertainties are the dominant source of systematic error in precision measurements at hadron colliders (e.g. $χ^2$ values of fits to extract $\sin^2θ_{eff}^{lept}(M_Z)$ from $A_{FB}(M,y)$ with different PDF replicas can be used to place additional constraints on PDFs.In turn, using these constrained PDFs significantly reduces the PDF errors in precision measurements of ele…
