Parton Contributions Research Articles

Spatial imaging of proton via leading-twist nonskewed GPDs with basis light-front quantization

The internal image of the proton is unveiled by examining the generalized parton distributions (GPDs) at zero skewness, within the basis light-front quantized environment. Several distributions emerge when a quark is sampled with different currents depending upon the helicity arrangements of the active quark and the proton target. We investigate six of the eight leading-twist proton GPDs of the valence quarks, the helicity conserving distributions (H,E,H˜) and the helicity nonconserving (HT,ET,H˜T) distributions at skewness set to zero (ζ=0). We consider purely transverse momentum transfer and, hence, obtain results describe only the proton’s two-dimensional structure in the transverse plane. We present the Mellin moments of these distribution functions, where the first moment produces a form factor and the second Mellin moments help extract the information on partonic contributions to the hadronic angular momentum. We compare our results for the Mellin moments with those from lattice QCD and other approaches where available. We also present the GPDs in transverse position space. Published by the American Physical Society 2024

P−p(p¯) cross section of isolated single photon production in the kt factorization and different angular ordering unintegrated parton distributions frameworks

In the present work, it is intended to calculate and study the single and double differential cross-sections of the prompt single-photon production as a function of produced single-photon transverse momentum and rapidity, in the high-energy P-P(\={P}) colliders, such as LHC and TEVATRON. The differential cross-sections of prompt single-photon production are calculated in the $k_t$-factorization frameworks using various angular ordering unintegrated parton distribution functions (UPDF), namely the Kimber et al. and Martin et al. procedures. These scheme-dependent UPDF are generated in the leading and next-to-leading order levels to predict and analyze the different partonic contributions to the above cross-sections. The above two procedures utilize the phenomenological parton distribution functions (PDF) libraries of Martin et al., i.e., MMHT2014. It is shown that the calculated prompt single-photon production differential cross-sections in the above frameworks are relatively successful in generating satisfactory results compared to the experimental data of different collaborations, i.e., CDF (2017), ATLAS (2017), CMS (2011) and D0 (2006), as well as the other theoretical predictions such as collinear factorization Monte Carlo calculations (the JETPHOX, SHERPA, PYTHIA, and MCFM methods). Also, for a closer precision, the differential cross-section for the NLO gluon-gluon , quark-gluon and quark-(anti)quark processes are calculated. An extensive discussion and comparison are made regarding (i) the behavior of the contributing partonic sub-processes, (ii) the possible double-counting between the $2\to 2$ and $2\to 3$ sub-processes, i.e., gluons-fusion, in our calculated prompt single-photon production differential cross-sections and (iii) the sensibility check of our results to the different angular ordering constraints.

Features of ω photoproduction off proton target at backward angles: Role of nucleon Reggeon in u -channel with parton contributions

Backward photoproduction of $\omega$ off a proton target is investigated in a Reggeized model where the $u$-channel nucleon Reggeon is constructed from the nucleon Born terms in a gauge invariant way. The $t$-channel meson exchanges are considered as a background. While the $N_\alpha$ trajectory of the nucleon Reggeon reproduces the overall shape of NINA data measured at the Daresbury Laboratory in the range of $u$-channel momentum transfer squared $-1.7<u<0.02$ GeV$^2$ and energies at $E_\gamma=2.8$, 3.5 and 4.7 GeV, a possibility of parton contributions is searched for through the nucleon isoscalar form factor which is parameterized in terms of parton distributions at the $\omega NN$ vertex. Detailed analysis is presented for NINA data to understand the reaction mechanism that could fill up the deep dip from the nucleon Reggeon at momentum squared $u=-0.15$ GeV$^2$. The angle dependence of differential cross sections at the NINA energies above are reproduced in the overall range of $u$ including the CLAS data at forward angles in addition. The energy dependence of the differential cross section is investigated based on the NINA data and the recent LEPS data. A feature of the present approach that implicates parton contributions via nucleon form factor is illustrated in the total and differential cross sections provided by GRAAL and CB-ELSA Collaborations.

The RHIC Spin Program Overview

After more than a decade of RHIC running as a polarized proton collider, we summarize recent achievements of the RHIC spin program and their impact on our understanding of the nucleon's spin structure, i.e. the individual parton (quarks and gluons) contributions to the helicity structure of the nucleon, and to understand the origin of the transverse spin phenomena. Open questions are identified and a suite of future measurements with polarized beams at RHIC to address them is laid out.

Charm contribution to bulk viscosity

In the range of temperatures reached in future heavy ion collision experiments, hadronic pair annihilations and creations of charm quarks may take place within the lifetime of the plasma. As a result, charm quarks may increase the bulk viscosity affecting the early stages of hydrodynamic expansion. Assuming thermalization, we estimate the charm contribution to bulk viscosity within the same effective kinetic theory framework in which the light parton contribution has been computed previously. The time scale at which this physics becomes relevant is related to the width of the transport peak associated with the trace anomaly correlator, and is found to be < 20 fm/c for T > 600 MeV.

The NNLO soft function for the pair invariant mass distribution of boosted top quarks

At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order (NNLO) corrections to the soft function appearing in this factorization formula, thus providing the final piece needed to evaluate at NNLO the differential cross section in the virtual plus soft approximation in the large invariant-mass limit. Technically, this amounts to evaluating the vacuum expectation value of a soft Wilson loop operator built out of light-like Wilson lines for each of the four partons participating in the hard scattering process, with a certain constraint on the total energy of the soft radiation. Our result turns out to be surprisingly simple, because in the sum of all graphs the three and four parton contributions multiply color structures whose coefficients are governed by the non-abelian exponentiation theorem.

Transverse polarization of the nucleon in parton picture

The protonʼs transverse polarization structure is examined in terms of the Lorentz-covariant Pauli–Lubanski vector in QCD. We find that there are contributions from leading, subleading, and next-to-subleading partonic contributions in the light-front system of coordinates. The subleading and next-to-subleading contributions are related to the leading one through Lorentz symmetry. And the leading contribution obeys a simple partonic angular momentum sum rule that gives a clear physical interpretation to a relation known previously.

Form factors of pseudoscalar mesons

We consider the transition (${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}^{0}(\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}\ensuremath{\gamma}$) and electromagnetic (${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$) form factors in a wide range of energy-momentum transfer $s$. We employ dispersion relations to connect the timelike and spacelike regions. We discuss the role of resonances and QCD partonic contributions. We find that the former give sizable contributions in the currently available range of $s$ and for the latter we consider the role of Reggeized fermion exchange.

Investigation of the parton structure of pomeron in b $\bar b$ -pair double-Pomeron-exchange production on the CMS (LHC)

Production of b \(\bar b\) -pairs in the process of hard double-Pomeron exchange (DPE) of protons has been studied on the CMS plant at the LHC accelerator energies of \(\sqrt s = 7\) TeV. The method for estimation of valent parton contribution in the Pomeron structure is developed. On the basis of H1 (DESY) data for parton distributions in Pomeron the calculations were performed to predict the hard (valent) parton components in the Pomeron structure. The contribution of valent partons is estimated about 61%. Using program package CMSSW, the event reconstruction of studied process also was made. This method can be applied to the available experimental data from the CMS detector.

What is double parton scattering?

Processes such as double Drell–Yan and same-sign WW production have contributions from double parton scattering, which are not well-defined because of a δ(2)(z⊥=0) singularity that is generated by QCD evolution. We study the single and double parton contributions to these processes, and show how to handle the singularity using factorization and operator renormalization. We compute the QCD evolution of double parton distribution functions (PDFs) due to mixing with single PDFs. The modified evolution of dPDFs at z⊥=0, including generalized dPDFs for the non-forward case, is given in Appendix A. We include a brief discussion of the experimental interpretation of dPDFs and how they can probe flavor, spin and color correlations of partons in hadrons.

High-energy photon-hadron scattering in holographic QCD

This article provides an in-depth look at hadron high-energy scattering by using gravity dual descriptions of strongly coupled gauge theories. Just like deeply inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) serve as clean experimental probes into nonperturbative internal structure of hadrons, elastic scattering amplitude of a hadron and a (virtual) photon in gravity dual can be exploited as a theoretical probe. Since the scattering amplitude at sufficiently high energy (small Bjorken $x$) is dominated by parton contributions ($=\mathrm{\text{Pomeron contributions}}$) even in strong coupling regime, there is a chance to learn a lesson for generalized parton distribution (GPD) by using gravity dual models. We begin with refining derivation of the Brower--Polchinski--Strassler--Tan (BPST) Pomeron kernel in gravity dual, paying particular attention to the role played by the complex spin variable $j$. The BPST Pomeron on warped spacetime consists of a Kaluza--Klein tower of 4D Pomerons with nonlinear trajectories, and we clarify the relation between Pomeron couplings and the Pomeron form factor. We emphasize that the saddle-point value ${j}^{*}$ of the scattering amplitude in the complex $j$-plane representation is a very important concept in understanding qualitative behavior of the scattering amplitude. The total Pomeron contribution to the scattering is decomposed into the saddle-point contribution and at most a finite number of pole contributions, and when the pole contributions are absent (which we call saddle-point phase), kinematical variable $(q,x,t)$-dependence of $\mathrm{ln}(1/q)$ evolution and $\mathrm{ln}(1/x)$ evolution parameters ${\ensuremath{\gamma}}_{\mathrm{eff}}$ and ${\ensuremath{\lambda}}_{\mathrm{eff}}$ in DIS and $t$-slope parameter $B$ of DVCS in HERA experiment are all reproduced qualitatively in gravity dual. All of these observations shed a new light on modeling of GPD. Straightforward application of those results to other hadron high-energy scattering is also discussed.

Azimuthal asymmetries for hadron distributions inside a jet in hadronic collisions

Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large-pT jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading unpolarized or (pseudo)scalar hadrons, namely pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) parton distribution and fragmentation functions, with special attention to the Sivers, Boer-Mulders, and transversity quark distributions, and to the Collins fragmentation function for quarks (and to the analogous functions for gluons). For each of these effects we evaluate, at central and forward rapidities and for kinematical configurations accessible at BNL-RHIC, the corresponding potentially maximized asymmetry (for pi+ production), obtained by saturating natural positivity bounds (and the Soffer bound for transversity) for the distribution and fragmentation functions involved and summing additively all partonic contributions. We then estimate, for both neutral and charged pions, the asymmetries involving TMD functions for which parameterizations are available. We also study the role of the different mechanisms, and the corresponding transverse single spin asymmetries, for large-pT inclusive jet production.

Characteristics and estimates of double parton scattering at the Large Hadron Collider

We evaluate the kinematic distributions in phase space of 4-parton final-state subprocesses produced by double parton scattering, and we contrast these with the final-state distributions that originate from conventional single parton scattering. Our goal is to establish the distinct topologies of events that arise from these two sources and to provide a methodology for experimental determination of the relative magnitude of the double parton and single parton contributions at Large Hadron Collider energies. We examine two cases in detail, the $b\overline{b}$ jet-jet and the 4 jet final states. After full parton-level simulations, we identify a few variables that separate the two contributions remarkably well, and we suggest their use experimentally for an empirical measurement of the relative cross section. We show that the double parton contribution falls off significantly more rapidly with the transverse momentum ${p}_{T}^{j1}$ of the leading jet, but, up to issues of the relative normalization, may be dominant at modest values of ${p}_{T}^{j1}$.

How the nuclear Fermi motion plus a simple statistical model explains the EMC effect

We present calculation of influence caused by nucleon Fermi motion on the parton distributions in nuclei. Our approach is based on the model where momenta of valence partons have some primordial distribution inside the hadron at rest, which is either provided by a statistical considerations or calculated using spherically symmetric Gaussian distribution with a width derived from the Heisenberg uncertainty relation. The sea parton contribution emerges from the similar Gaussian distribution with a width dictated by the presence of virtual pions in hadron. We show that the influence of Fermi motion changes substantially the nucleonic structure function inside the nucleus in the right direction and therefore should be considered seriously in all attempts devoted to explain the experimentally observed EMC effect for x Bj > 0.1.

Summary WG2 Part 1a: using neutrinos to study partons in the nucleon and the nucleus at the neutrino factory

A neutrino deep-inelastic scattering experiment at a neutrino factory is described. The improvements possible in extracting parton distribution functions both within the nucleon and the nuclear environment are shown. The intriguing possibility of using (anti)neutrino scattering off a polarized target to determine the individual partonic spin contributions to the nucleon is discussed.

Four jet event shapes in electron-positron annihilation

We report next-to-leading order perturbative QCD predictions of 4 jet event shape variables for the process $e^+e^-\to\rm{4\,\,jets}$ obtained using the general purpose Monte Carlo EERAD2. This program is based on the known `squared' one loop matrix elements for the virtual $\gamma^* \to 4$ parton contribution and squared matrix elements for 5 parton production. To combine the two distinct final states numerically we present a hybrid of the commonly used subtraction and slicing schemes based on the colour antenna structure of the final state which can be readily applied to other processes. We have checked that the numerical results obtained with EERAD2 are consistent with next-to-leading order estimates of the distributions of previously determined four jet-like event variables. We also report the next-to-leading order scale independent coefficients for some previously uncalculated observables; the light hemisphere mass, narrow jet broadening and the 4 jet transition variables with respect to the JADE and Geneva jet finding algorithms. For each of these observables, the next-to-leading order corrections calculated at the physical scale significantly increase the rate compared to leading order (the K factor is approximately 1.5–2). With the exception of the 4 jet transition variables, the published DELPHI data lies well above the ${\cal O}(\alpha_s^3)$ predictions. The renormalisation scale uncertainty is still large and in most cases the data prefers a scale significantly smaller than the physical scale. This situation is reminiscent of that for three jet shape variables, and should be improved by the inclusion of power corrections and resummation of large infrared logarithms.

Reaction dynamics in Pb + Pb at the CERN/SPS: From partonic degrees of freedom to freeze-out

We analyze the reaction dynamics of central Pb+Pb collisions at 160 GeV/nucleon. First we estimate the energy density e pile-up at mid-rapidity and calculate its excitation function: ε is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for E lab ⩾ 30GeV/nucleon . The energy density reaches up to 4 GeV/fm 3, 95% of which are contained in partonic degrees of freedom. It is shown that cells of hadronic matter, after t ≈ 2R/γν cm can be viewed as nearly chemically equilibrated. This matter never exceeds energy densities of ∼ 0.4 GeV/fm 3, i.e. a density above which the notion of separated hadrons loses its meaning. The final reaction stage is analyzed in terms of hadron ratios, freeze-out distributions and a source analysis for final state pions.

Excitation function of energy density and partonic degrees of freedom in relativistic heavy ion collisions

We estimate the energy density ϵ pile-up at mid-rapidity in central Pb+Pb collisions from 2–200 GeV/nucleon. ϵ is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for E lab≥30 GeV/nucleon. In Pb+Pb collisions at 160 GeV/nucleon the energy density reaches up to 4 GeV/fm 3, 95% of which are contained in partonic degrees of freedom.

Open charm, photon, and dilepton production in an increasingly strongly interacting parton plasma

We examine the effects that the new equilibration scenario of the increasingly strongly interacting parton plasma and the nonequilibrium environment have on the production of open charms, photons, and dileptons at Large Hadron Collider (LHC) and at Relativistic Heavy Ion Collider (RHIC) energies. We show that an out-of-equilibrium effect, not shown before, changes significantly the relative yield of the two main partonic contributions to photon production in the higher ${p}_{T}$ range, and higher orders for electromagnetic emissions have increased significance in the new scenario especially at RHIC energies. We argue that the effects of the new scenario are not restricted just to the parton phase but will continue through to the later hadron gas phase with potentially positive implications for the detection of the quark-gluon plasma.

Shadowing in inelastic lepton-deuteron scattering

Shadowing in inelastic lepton-deuteron scattering is analysed using the double interaction formalism where we relate shadowing to inclusive diffractive processes. Both the vector meson and parton contributions are considered for low and high Q 2 values including QCD corrections with parton recombination for high Q 2. These Q 2 values were chosen to correspond to existing experimental data and to the possible HERA measurements. Detailed discussion of various shadowing mechanisms is given. As expected the shadowing effects are found to be very small, less then 2% or so, in agreement with the recent precise measurements performed by the New Muon Collaboration. The contribution of shadowing terms to the Gottfried sum from the region x > 0.004 and for Q 2 = 4 GeV 2 is estimated to be equal to −0.025.