Quark Parton Research Articles

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb gauge

Abstract Recently, it has been proposed to compute parton distributions from boosted correlators fixed in the Coulomb gauge within the framework of Large-Momentum Effective Theory. This method does not involve Wilson lines and could greatly improve the efficiency and precision of lattice QCD calculations. However, there are concerns about whether the systematic uncertainties from Gribov copies, which correspond to the ambiguity in lattice gauge-fixing, are under control. This work gives an assessment of the Gribov copies’ effect in the Coulomb-gauge-fixed quark correlators. We utilize different strategies for the Coulomb-gauge fixing, selecting two different groups of Gribov copies based on the lattice gauge configurations. We test the difference in the resulted spatial quark correlators in the vacuum and a pion state. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise. This demonstrates that the effect of the Gribov copies can be neglected in the practical lattice calculation of the quark parton distributions.

Orbital angular momentum small-x evolution: exact results in the large-Nc limit

We construct an exact solution to the revised small-x orbital angular momentum (OAM) evolution equations derived in [1], based on an earlier work [2]. These equations are derived in the double logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant and x the Bjorken x variable) and the large-Nc limit, with Nc the number of quark colors. From our solution, we extract the small-x, large-Nc expressions of the quark and gluon OAM distributions. Additionally, we determine the large-Nc small-x asymptotics of the OAM distributions to beLq+q¯xQ2∼LGxQ2∼ΔΣxQ2∼ΔGxQ2∼1xαh,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{q+\\overline{q}}\\left(x,{Q}^2\\right)\\sim {L}_G\\left(x,{Q}^2\\right)\\sim \\Delta \\Sigma \\left(x,{Q}^2\\right)\\sim \\Delta G\\left(x,{Q}^2\\right)\\sim {\\left(\\frac{1}{x}\\right)}^{\\alpha_h}, $$\\end{document}with the intercept αh the same as obtained in the small-x helicity evolution [3], which can be approximated as αh ≈ 3.66074αsNc2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 3.66074\\sqrt{\\frac{\\alpha_s{N}_c}{2\\pi }} $$\\end{document}. This result is in complete agreement with [4]. Additionally, we calculate the ratio of the quark and gluon OAM distributions to the flavor-singlet quark and gluon helicity parton distribution functions respectively in the small-x region.

Precise QCD predictions for W-boson production in association with a charm jet

The production of a W-boson with a charm quark jet provides a highly sensitive probe of the strange quark distribution in the proton. Employing a novel flavour dressing procedure to define charm quark jets, we compute W+charm-jet production up to next-to-next-to-leading order (NNLO) in QCD. We study the perturbative stability of production cross sections with same-sign and opposite-sign charge combinations for the W boson and the charm jet. A detailed breakdown according to different partonic initial states allows us to identify particularly suitable observables for the study of the quark parton distributions of different flavours.

Quark and gluon distributions in ρ-meson from basis light-front quantization

We solve for the ρ-meson's wave functions from a light-front QCD Hamiltonian determined for its constituent quark-antiquark and quark-antiquark-gluon Fock components, with a three-dimensional confinement using basis light-front quantization. From this, we obtain the leading-twist valence quark's parton distribution functions and transverse momentum-dependent parton distributions inside the ρ-meson. These results are qualitatively consistent with those of other models. We also demonstrate the important effects of a dynamical gluon on the ρ-meson's gluon densities, helicity, transversity, and tensor polarized distributions.

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ2. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

Boost asymmetry of the diboson productions in pp collisions

We propose the boost asymmetry of the diboson productions in pp collisions as a new experimental observable, which can provide unique information on the proton structure. The boost asymmetry rises as the difference in the kinematics of the two bosons, that are coupled to the two different quark and antiquark initial states, respectively, and thus reflects different features of the quark and antiquark parton densities. By comparing the kinematics of the two bosons, such as the boson energy or rapidity, the diboson events with antiquark having higher energy than quark can be distinguished from those with quark having higher energy than antiquark. This would provide unique information in some special parton momentum fraction regions, which cannot be directly proved by current W and Z measurements at the Large Hadron Collider or other deep inelastic scattering experients.

Impact of W and Z Production Data and Compatibility of Neutrino DIS Data in Nuclear Parton Distribution Functions

Vector boson production and neutrino deep-inelastic scattering (DIS) data are crucial for constraining the strange quark parton distribution function (PDF) and more generally for flavor decomposition in PDF extractions. We extend the nCTEQ15 nuclear PDFs (nPDFs) by adding the recent W and Z production data from the LHC in a global nPDF fit. The new nPDF set, referred to as nCTEQ15WZ, is used as a starting point for a follow-up study in which we assess the compatibility of neutrino DIS data with charged lepton DIS data. Specifically, we re-analyze neutrino DIS data from NuTeV, Chorus, and CDHSW, as well as dimuon data from CCFR and NuTeV. To scrutinize the level of compatibility, different kinematic regions of the neutrino data are investigated. Fits to the neutrino data alone and a preliminary global fit are performed and compared to nCTEQ15WZ.

Parton rescattering and gluon saturation in dijet production at EIC

Large angle gluon radiations induced by multiple parton scatterings contribute to dijet production in deeply inelastic scattering off a large nucleus at the Electron-Ion Collider. Within the generalized high-twist approach to multiple parton scattering, such contributions at the leading order in perturbative QCD and large Bjorken momentum fraction $x_B$ can be expressed as a convolution of the multiple parton scattering amplitudes and the transverse momentum dependent (TMD) two-parton correlation matrix elements. We study this medium-induced dijet spectrum and its azimuthal angle correlation under the approximation of small longitudinal momentum transfer in the secondary scattering and the factorization of two-parton correlation matrix elements as a product of quark and gluon TMD parton distribution function (PDF). Using a simple model for gluon saturation based on the parametrized gluon TMD PDF, we can calculate the $x_B$ and $Q^2$ dependence of the saturation scale and parton transport coefficient $\hat q$. Contributions to dijet cross section from double scattering are power-suppressed and only become sizable for mini-jets at small transverse momentum. We find that the total dijet correlation for these mini-jets, which also includes the contribution from single scattering, is sensitive to the transverse momentum broadening in the quark TMD PDF at large $x$ and saturation in the gluon TMD PDF at small $x$ inside the nucleus. The correlation from double scattering is also found to increase with the dijet rapidity gap and have a quadratic nuclear-size dependence because of the Landau-Pomeranchuk-Migdal (LPM) interference in gluon emission induced by multiple scattering. Experimental measurements of such unique features in the dijet correlation can shed light on the LPM interference in strong interaction and gluon saturation in large nuclei.

Proton mass decomposition and hadron cosmological constant

Lattice results on sigma terms and global analysis of parton momentum fractions are used to give the quark and glue fractions of the proton mass and rest energy. The mass decomposition in terms of the trace of the energy-momentum tensor is renormalization group invariant. The decomposition of the rest energy from the Hamiltonian and the gravitational form factors are scheme and scale dependent. The separation of the energy-momentum tensor into the traceless part, which is composed of the quark and glue parton momentum fractions, and the trace part has the minimum scheme dependence. We identify the glue part of the trace anomaly $⟨{H}_{\ensuremath{\beta}}⟩$ as the vacuum energy from the glue condensate in the vacuum. From the metric term of the gravitational form factors, which is the stress part of the stress-energy-momentum tensor, we find that the trace part of the rest energy, dominated by $⟨{H}_{\ensuremath{\beta}}⟩$, gives a constant restoring pressure that balances that from the traceless part of the Hamiltonian to confine the hadron, much like the cosmological constant Einstein introduced for a static universe. From a lattice calculation of $⟨{H}_{\ensuremath{\beta}}⟩$ in the charmonium, we deduce the associated string tension, which turns out to be in good agreement with that from a Cornell potential, which fits the charmonium spectrum.

Gluon PDF from quark dressing in the nucleon and pion

Gluon dressing of the light quarks within hadrons is very strong and extremely important in that it dynamically generates most of the observable mass through the breaking of chiral symmetry. The quark and gluon parton densities, q(x) and g(x), are necessarily interrelated since any gluon emission and absorption process, especially dressing of a quark, contributes to g(x) and modifies q(x). Guided by long-established results for the parton-in-parton distributions from a strict 1-loop perturbative analysis of a quark target, we extend the non-perturbative QCD approach based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations to describe the interrelated valence qv(x) and the dressing-gluon g(x) for a hadron at its intrinsic model scale. We employ the pion description from previous DSE work that accounted for the gluon-in-quark effect, and introduce a simple model of the nucleon for exploratory purposes. We find typically 〈x〉g∼0.20 for both pion and nucleon at the model scale, and the valence quark helicity contributes 52% of nucleon spin. We deduce both qv(x) and g(x) from 30 calculated Mellin moments, and after adopting existing data analysis results for qsea(x), we find that NLO scale evolution produces g(x) in good agreement with existing data analysis results for the pion at 1.3 GeV and the nucleon at 5 GeV2. At the scale 2 GeV typical of lattice-QCD calculations, we obtain 〈x〉gN=0.42 in good agreement with 0.38 from the average of recent lattice-QCD calculations.

Reinterpretation of proton strangeness between ATLAS and CMS measurements

We reexamine the shapes of the strange quark parton distribution functions (PDFs) of the proton by means of quantum chromodynamics (QCD) analysis of {\hera} deep inelastic scattering cross section measurement at DESY, and inclusive gauge boson production and $W$ boson production associated with a charm quark from LHC at CERN. We find that there is an overall agreement on the strange quark distributions obtained from CMS $W$ + charm and ATLAS $W/Z$ data at the parton momentum fraction range $x \lesssim 10^{-2}$. Meanwhile, there is also a strong tension between these data towards large $x$. We find that this tension fades away if the ATLAS measurement of $W/Z$ production is analyzed together with the ATLAS $W$ + charm data. The $W/Z$ and $W$ + charm data both from ATLAS and CMS experiments agree that the proton strangeness is enhanced towards small momentum fraction $x$ and is smoothly suppressed at large $x$. Furthermore, a strong $x$ dependence of the strange-to-non-strange parton ratio $R_s(x,Q^2)$ is observed.

Flavor decomposition of the nucleon unpolarized, helicity, and transversity parton distribution functions from lattice QCD simulations

We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost. We find non-zero results for the disconnected isoscalar and strange quark distributions. The determination of the quark parton distribution and in particular the strange quark contributions that are poorly known provide valuable input to the structure of the nucleon.

Parton distributions in the SMEFT from high-energy Drell-Yan tails

The high-energy tails of charged- and neutral-current Drell-Yan processes provide important constraints on the light quark and anti-quark parton distribution functions (PDFs) in the large-x region. At the same time, short-distance new physics effects such as those encoded by the Standard Model Effective Field Theory (SMEFT) would induce smooth distortions to the same high-energy Drell-Yan tails. In this work, we assess for the first time the interplay between PDFs and EFT effects for high-mass Drell-Yan processes at the LHC and quantify the impact that the consistent joint determination of PDFs and Wilson coefficients has on the bounds derived for the latter. We consider two well-motivated new physics scenarios: 1) electroweak oblique corrections ( hat{W},hat{Y} ) and 2) four-fermion interactions potentially related to the LHCb anomalies in R(K(*)). We account for available Drell-Yan data, both from unfolded cross sections and from searches, and carry out dedicated projections for the High-Luminosity LHC. Our main finding is that, while the interplay between PDFs and EFT effects remains moderate for the current dataset, it will become a significant challenge for EFT analyses at the HL-LHC.

The strangest proton?

We present an improved determination of the strange quark and antiquark parton distribution functions of the proton by means of a global QCD analysis that takes into account a comprehensive set of strangeness-sensitive measurements: charm-tagged cross sections for fixed-target neutrino–nucleus deep-inelastic scattering, and cross sections for inclusive gauge-boson production and W-boson production in association with light jets or charm quarks at hadron colliders. Our analysis is accurate to next-to-next-to-leading order in perturbative QCD where available, and specifically includes charm-quark mass corrections to neutrino–nucleus structure functions. We find that a good overall description of the input dataset can be achieved and that a strangeness moderately suppressed in comparison to the rest of the light sea quarks is strongly favored by the global analysis.

Impact of LHC vector boson production in heavy ion collisions on strange PDFs

The extraction of the strange quark parton distribution function (PDF) poses a long-standing puzzle. Measurements from neutrino-nucleus deep inelastic scattering (DIS) experiments suggest the strange quark is suppressed compared to the light sea quarks, while recent studies of W^pm /Z boson production at the LHC imply a larger strange component at small x values. As the parton flavor determination in the proton depends on nuclear corrections, e.g. from heavy-target DIS, LHC heavy ion measurements can provide a distinct perspective to help clarify this situation. In this investigation we extend the nCTEQ15 nPDFs to study the impact of the LHC proton-lead W^pm /Z production data on both the flavor differentiation and nuclear corrections. This complementary data set provides new insights on both the LHC W^pm /Z proton analyses and the neutrino-nucleus DIS data. We identify these new nPDFs as nCTEQ15WZ. Our calculations are performed using a new implementation of the nCTEQ code (nCTEQ++) based on C++ which enables us to easily interface to external programs such as HOPPET, APPLgrid and MCFM. Our results indicate that, as suggested by the proton data, the small x nuclear strange sea appears larger than previously expected, even when the normalization of the W^{pm }/Z data is accommodated in the fit. Extending the nCTEQ15 analysis to include LHC W^pm /Z data represents an important step as we advance toward the next generation of nPDFs.

Transverse momentum dependent PDFs at N3LO

We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.

Bogolyubov–Medvedev–Polivanov S-matrix Method and Its Application to Multi-Particle Systems and in High-Energy Physics

The connection between field-theoretic equations based on the Bogolyubov–Medvedev–Polivanov and Lehman–Szymanczyk–Zimmerman $$S$$ -matrix methods is discussed [1]. These equations are used to derive three-dimensional time-ordered relativistic Lippmann–Schwinger-type equations for hadronic collision amplitudes with and without quark degrees of freedom [2, 3]. Quark degrees of freedom are considered following the Huang–Weldon approach [4], in which hadrons are considered as bound states of quarks. Numerical solutions of the obtained equations made it possible to describe well the experimental phase shifts of elastic $$\pi N$$ and $$NN$$ scattering in the low-energy region. Using a separable approximation, a quark–parton model for inclusive production of particles with a large transverse momentum was reproduced [6]. This made it possible to describe the experimental data of inclusive production of a $$\rho $$ meson with a large transverse momentum (≤1.5 GeV/c) in a proton–proton collision in the energy region 2.9 ≤ $$\sqrt s $$ ≤ 64 GeV [5].

Heavy quark diffusion in a Polyakov loop plasma

We calculate the transport coefficients, drag and momentum diffusion, of a heavy quark in a thermalized plasma of light quarks in the background of Polyakov loop. Quark thermal mass and the gluon Debye mass are calculated in a non-trivial Polyakov loop background. The constituent quark masses and the Polyakov loop is estimated within a Polyakov loop quark meson (PQM) model. The relevant scattering amplitudes for heavy quark and light partons in the background of Polyakov loop has been estimated within the matrix model. We have also compared the results with the Polyakov loop parameter estimated from lattice QCD simulations. We have studied the temperature and momentum dependence of heavy quark drag and diffusion coefficients. It is observed that the temperature dependence of the drag coefficient is quite weak which may play a key role to understand heavy quark observables at RHIC and LHC energies.

Small- x helicity evolution: An operator treatment

We rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we re-derive the double-logarithmic small-$x$ evolution equations for quark helicity in terms of the "polarized Wilson lines", the operators consisting of light-cone Wilson lines with one or two non-eikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark sub-eikonal operators. We show that the double-logarithmic small-$x$ evolution of the "polarized dipole amplitude" operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-$x$ asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity.

The twist-three distribution eq(x,k⊥) in a light-front model

We discuss the twist-three, unpolarized, chiral-odd, transverse momentum dependent parton distribution (TMD) eq(x,k⊥) within a light-front model. We review a model-independent decomposition of this TMD, which follows from the QCD equations of motion and is given in terms of a mass term, a pure interaction-dependent contribution, and singular terms. The mass-term and pure twist-three contributions are represented in terms of overlap of light-front wave functions (LFWFs), taking into account the Fock states with three valence quark (3q) and three-quark plus one gluon (3q+g). The 3q and 3q+g LFWFs with total orbital angular momentum zero are modeled using a parametrization derived from the conformal expansion of the proton distribution amplitudes, with parameters fitted to reproduce available phenomenological information on the unpolarized leading-twist quark and gluon collinear parton distributions. Numerical predictions for both the quark TMD eq(x,k⊥) and the collinear parton distribution eq(x) are presented, discussing the role of the quark–gluon correlations in the proton.