We propose a new method to determine the spatially or impact-parameter dependent nuclear parton distribution functions (nPDFs) using the double parton scattering (DPS) processes in high-energy heavy-ion (proton-nucleus and nucleus-nucleus) collisions. We derive a simple generic DPS formula in nuclear collisions by accommodating both the nuclear collision geometry and the spatially dependent nuclear modification effect, under the assumption that the impact-parameter dependence of nPDFs is only related to the nuclear thickness function. While the geometric effect is widely adopted, the impact of the spatially dependent nuclear modification on DPS cross sections has been overlooked so far, which can, however, be significant when the initial nuclear modification is large. In turn, the DPS cross sections in heavy-ion collisions can provide useful information on the spatial dependence of nPDFs. They can be, in general, obtained in minimum-bias nuclear collisions, featuring the virtue of independence of Glauber modeling.
We study in the framework of collinear QCD factorization the photoproduction of a $γ\,π$ pair with a large invariant mass and a small transverse momentum, as a new way to access generalized parton distributions. In the kinematics of JLab 12-GeV, we demonstrate the feasibility of this measurement and show the extreme sensitivity of the unpolarized cross section to the axial quark GPDs.
Exclusive photoproduction of a $γ\,π^\pm$ pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum is described in the collinear factorization framework. The scattering amplitude is calculated at leading order in $α_s$ and the differential cross sections for the process are estimated in the kinematics of the JLab~12-GeV experiments. The order of magnitude of the predicted cross-sections seems sufficient for a dedicated experiment to be performed. The process turns out to be very sensitive to the axial generalized parton distribution…
A short review of form factors, parton distribution functions and generalized parton distributions is given. A possible application of generalized parton distributions in the weak sector is discussed.
Spin-dependent quark densities, matrix elements of specific density operators in proton states of definite spin-polarization, indicate that the nucleon may harbor an infinite variety of non-spherical shapes. We show that these matrix elements are closely related to specific transverse momentum dependent parton distributions accessible in the angular dependence of the semi-inclusive processes electron plus proton goes to electron plus pion plus anything, and the Drell-Yan reaction proton plus proton goes to a lepton anti-lepton pair plus anything. New measurements or analyses would allow the di…
Exclusive electroproduction of a K or K* meson on the nucleon can give a Theta+ pentaquark in the final state. This reaction offers an opportunity to investigate the structure of pentaquark baryons at parton level. We discuss the generalized parton distributions for the N-->Theta+ transition and give the leading order amplitude for electroproduction in the Bjorken regime. Different production channels contain complementary information about the distribution of partons in a pentaquark compared with their distribution in the nucleon. Measurement of these processes may thus provide deeper insight…
We calculate and compare the differential cross sections for forward $Z^0$-boson production at small transverse momentum, in proton-proton and proton-nucleus collisions, using both the collinear and dilute-dense factorization frameworks. In both cases, we implement a Sudakov resummation of the large logarithms generated by soft-gluon emissions, which is essential in order to describe the transverse momentum distribution of forward $Z^0$ bosons measured at the Tevatron and the LHC. We further compute the nuclear modification factor in the dilute-dense framework, hoping to single out signals of …
Heavy ion collisions provide a unique probe of the quark-gluon plasma properties. The role of partonic degrees of freedom in p-Pb collisions at $\sqrt{s_{NN}}$ = 5 TeV by studying the production cross section is studied. Experimental observable like the number of K$_S$ mesons is sensitive to the kinematic properties of the reaction. Our results demonstrate the importance of angular distribution for the partonic degrees of freedom in hadronization process.
While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured …
We study the exclusive reactions pi- p -> l+ l- n and pi+ n -> l+ l- p$ in view of possible future experiments with high-intensity pion beams. For large invariant mass of the lepton pair l+ l- and small squared momentum transfer to the nucleon these are hard-scattering processes providing access to generalized parton distributions. We estimate the cross section for these reactions, explore their connection with the pion form factor, and discuss the role they can play in improving our understanding of the relevant reaction mechanisms.
We calculate production rates for several hard processes in ultraperipheral proton-nucleus and nucleus-nucleus collisions at the LHC. The resulting high rates demonstrate that some key directions in small $x$ research proposed for HERA will be accessible at the LHC through these ultraperipheral processes. Indeed, these measurements can extend the HERA $x$ range by roughly a factor of 10 for similar virtualities. Nonlinear effects on the parton densities will thus be significantly more important in these collisions than at HERA.
A dedicated test of the perturbative QCD NLO parton evolution in the very small-$x$ region is performed. We find a good agreement with recent precision HERA-data for $F_2^p(x,Q^2)$, as well as with the present determination of the curvature of $F_2^p$. Characteristically, perturbative QCD evolutions result in a positive curvature which increases as $x$ decreases. Future precision measurements in the very small $x$-region, $x<10^{-4}$, could provide a sensitive test of the range of validity of perturbative QCD
Recent experimental and theoretical results presented in the working group "Parton densities from DIS and hadron colliders to LHC" at the DIS2010 workshop are summarized in this contribution.
I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation func- tions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.
Different methods to extract the polarized parton densities from the world polarized DIS data are considered. The higher twist corrections $h^N(x)/Q^2$ to the spin dependent proton and neutron $g_1$ structure functions are found to be non-negligible and important in the QCD analysis of the present experimental data. Their role in determining the polarized parton densities in the framework of the different approaches is discussed.
The impact of positivity constraints on the polarized parton densities has been studied. Special attention has been paid to the role of positivity constraints in determining the polarized strange quark and gluon densities, which are not well determined from the present data on inclusive polarized DIS.
We evaluate the differential cross section for the electroproduction of lepton pairs off a polarized nucleon target in the generalized Bjorken region to leading power accuracy in hard momentum. We discuss the importance of this process for phenomenology of generalized parton distributions. A special attention is given to the sensitivity of physical observables, i.e., diverse asymmetries, to their dependence on scaling variables that allows to map directly the functional two-dimensional surface of generalized parton distributions.
Spin and transverse momentum dependent parton distributions - Generalized Parton Distributions (GPDs) - are at the interface between the QCD structure of the hadrons and observable quantities. The GPDs are linear superpositions within helicity amplitudes. The amplitudes are probed in high energy leptoproduction processes through angular dependent cross sections and polarization asymmetries. Phenomenological extraction of the amplitudes and the distributions is a challenging task. We present observables that connect particularly with the chiral odd quark-nucleon helicity amplitudes for Deeply V…
Associated with the use of conventional integrated parton densities are kinematic approximations on parton momenta which result in unphysical differential distributions for final-state particles. We argue that it is important to reformulate perturbative QCD results in terms of fully unintegrated parton densities, differential in all components of the parton momentum.
The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.
We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing t…
We investigate the role of partonic degrees of freedom in high multiplicity p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV carried out at the Large Hadron Collider (LHC) by studying the production and collective flow of identified hadrons at intermediate $p_T$ via the coalescence of soft and hard partons generated from viscous hydrodynamics (VISH2+1) and the energy loss model (LBT), respectively. We find that combining the intermediate $p_T$ hadrons from the coalescence with the low $p_T$ hadrons from hydrodynamics and high $p_T$ hadrons from the jet fragmentation, our Hydro-Coal-Frag model prov…
In this talk we summarize main results of a recent determination of the polarized deeply inelastic parton distributions to NLO from the world data. In the analysis the LO and NLO parton densities and their $1σ$ statistical errors were derived and parameterized. The strong coupling constant $α_s(M_Z^2)$ is determined $α_s(M_Z^2) = 0.113 \pm 0.004 {\rm (stat.)} \pm~0.004 {\rm (fac.)} +0.008/-0.005 {\rm (ren.)}$ Comparisons of the low moments of the parton densities with recent lattice results are given. A detailed error-analysis of the gluon density is performed.
In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively-calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the $H_q(x,ξ,t)$ distribution for the pion and proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result ca…
We propose the study of unpolarized transverse momentum dependent gluon parton distributions as well as the effect of linearly polarized gluons on transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ production within the framework of transverse momentum dependent factorization employing color evaporation model (CEM) in unpolarized proton-proton collision. We estimate the transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ at LHCb, RHIC and AFTER energies using TMD evolution formalism.
An accurate knowledge of nuclear parton distribution functions (nPDFs) is an essential ingredient of high energy physics calculations when the processes are involving nuclei in the initial state. It is well known now that the prompt photon production both in hadronic and nuclear collisions is a powerful tool for exploring the parton densities in the nucleon and nuclei especially of the gluon. In this work, we are going to perform a comprehensive study of the isolated prompt photon production in $ p $-Pb collisions at backward rapidities to find the best kinematic regions in which the experimen…
New fragmentation functions (FFs) are extracted from a NLO QCD fit to the preliminary COMPASS data on pion and kaon multiplicities. It is shown that the new kaon FFs are very different from those of De Florian at al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.
The feasibility of an experimental determination of the parton distributions of virtual photons at high energy $ep$ colliders is studied in the context of the DESY-HERA collider. Recently proposed parton densities of virtual photons are utilized to evaluate the appropriate production processes and their relevant kinematical regions. It is demonstrated that high $E_T$ jet production with $E_T\,\simeq 5-7\, {\rm{GeV}}$ and $b\bar{b}$ production can probe the parton distributions of virtual photons up to virtualities of a few ${\rm{GeV}}^2$. A useful leading order parametrization of our proposed …
We perform a comprehensive new Monte Carlo analysis of high-energy lepton-lepton, lepton-hadron and hadron-hadron scattering data to simultaneously determine parton distribution functions (PDFs) in the proton and parton to hadron fragmentation functions (FFs). The analysis includes all available semi-inclusive deep-inelastic scattering and single-inclusive $e^+ e^-$ annihilation data for pions, kaons and unidentified charged hadrons, which allows the flavor dependence of the fragmentation functions to be constrained. Employing a new multi-step fitting strategy and more flexible parametrization…
Recently, the ZEUS collaboration has reported on several remarkable properties of events with a large rapidity gap in deep inelastic scattering. We suggest that the mechanism underlying these events is the scattering of electrons off lumps of wee partons inside the proton. Based on an effective lagrangian approach the $Q^2$-, $x$- and $W$-distributions are evaluated. For sufficiently small invariant mass of the detected hadronic system, the mechanism implies leading twist behaviour. The $x$- and $W$-distributions are determined by the Lipatov exponent which governs the behaviour of parton dens…
The present status of the longitudinal polarized parton densities (PDFs) and the contribution of their first moments to the nucleon spin is discussed. Special attention is paid to the role of higher twist effects in determining the PDFs and to the polarized strange quark and gluon densities, which are still not well determined from the present data.
Collinear and transverse momentum dependent (TMD) parton densities are obtained from fits to precision measurements of deep inelastic scattering (DIS) cross sections at HERA. The parton densities are evolved by DGLAP evolution with next-to-leading-order (NLO) splitting functions using the parton branching method, allowing one to determine simultaneously collinear and TMD densities for all flavors over a wide range in $x$, $μ^2$ and $k_t$, relevant for predictions at the LHC. The DIS cross section is computed from the parton densities using perturbative NLO coefficient functions. Parton densiti…
We show that the enhancement of the saturation scale in large nuclei relative to the proton is significantly influenced by the effects of quantum evolution and the impact parameter dependence of dipole cross sections in high energy QCD. We demonstrate that there is a strong A dependence in diffractive deeply inelastic scattering and discuss its sensitivity to the measurement of the recoil nucleus.
Generalized parton distributions (GPDs) enter QCD factorization theorems for hard exclusive reactions. They encode rich information about hadron partonic structure. We explore a possibility to constrain GPDs in experiments at LHC considering two different exclusive processes: the timelike Compton scattering and the photoproduction of heavy vector mesons.
Rapidity divergences occur when parton densities in a gauge theory are defined in the most natural way, as expectation values of partonic number operators in light-front quantization. I review these and other related divergences, and show how the definitions of parton densities can be modified to remove the divergences. A modified definition is not only essential for many phenomenological applications of QCD, but also concerns the treatment of parton densities in non-perturbative approaches. The necessity of modifications in the definition of a parton density also entails corrections in the fo…
We present a new leading and next-to-leading QCD analysis of the world data on inclusive polarized deep inelastic scattering. A new set of polarized parton densities is extracted from the data and the sensitivity of the results to the newly incorporated SLAC/E155 proton data is discussed.
We analyze the time-like processes gamma gamma -> B Bbar and p p-bar -> gamma M at large Mandelstam variables within the handbag approach for which the process amplitudes factorize in hard partonic subprocesses and annihilation form factor. The latter represent moments of baryon-antibaryon generalized parton distributions. Symmetry relations restrict the number of independent annihilation form factors for the ground state baryons drastically. We determine these form factors from the present BELLE data on gamma gamma -> B Bbar with the help of simplifying assumptions. The knowledge of these for…
Polarization asymmetries in photoproduction of high transverse momentum mesons are a flavor sensitive way to measure the polarized quark distributions. We calculate the expected asymmetries in several models, and find that the asymmetries are significant and also significantly different from model to model. Suitable data may come as a by-product of deep inelastic experiments to measure $g_1$ or from dedicated experiments.
We present a determination of parton densities at NLO obtained with the Parton Branching method using precision measurements of deep inelastic scattering cross sections at HERA. The two sets of parton densities shown in this work are obtained with the same angular angular ordering condition for the evolution scale and they differ in the chosen scale for the strong coupling evaluation, for which we consider two scenarios: the evolution scale, and the transverse momentum qT from the angular ordering prescription. The transverse momentum dependent densities obtained with the Parton Branching meth…
The parton densities of the proton are of fundamental importance not only for our description of hadronic and nuclear structure, but also for reliable predictions for new heavy particle searches at colliders. At the large partonic momentum fractions required for the production of these particles, the parton distribution functions, in particular the one of the gluon, are unfortunately still badly constrained. In this paper, we investigate the possibility to improve on their determination with new data coming from electroweak vector boson production at large transverse momenta at the LHC with ce…
A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the CASCADE package for the full TMD parton shower, final state shower and…
I give an account of a new definition of transverse-momentum-dependent parton densities. The new definition solves a number of difficulties and inconsistencies in earlier definitions.
We present calculations of several pp scattering cross sections with potential applications at the LHC. Significantly large rates for momentum fraction, x, as low as 10^-7 are obtained, allowing for possible extraction of quark and gluon densities in the proton and nuclei down to these small x values provided a detector with good acceptance at maximal rapidities is used.
There have been recent debates about whether $\overline{\text{MS}}$ parton densities exactly obey positivity bounds (including the Soffer bound), and whether the bounds should be applied as a constraint on global fits to parton densities and on nonperturbative calculations. A recent paper (JHEP ${\bf \text{11}}$ (2020) 129) appears to provide a proof of positivity in contradiction with earlier work by other authors. We examine their derivation and find that its primary failure is in the apparently uncontroversial statement that bare pdfs are always positive. We show that under the conditions u…
A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the spin--structure of nucleons in the future.
We review the current status of collinear and Transverse Momentum Dependent densities based on the Parton Branching method. We investigate the performance of the PB-TMD evolution as well as PB-TMD parton shower with different configurations of the hard process in the four- and five-flavour schemes.
We have re-analyzed the world data on inclusive polarized DIS, in both NLO and LO QCD, including the new HERMES and COMPASS data. The updated NLO polarized densities are given in both the $\rm \bar{MS}$ and JET schemes. The impact of the new data on the results is discussed.
In the paper we include Bose-Einsten correlations for identical gluons, in the evolution of the double parton densities at low $x$ (high energies). We show that these correlations result in a faster increase of the double densities, in comparison with the product of two single parton densities. In addition, we find that the typical momentum in the double parton cross section, is of the order of the hard scales in the process, including the saturation momentum. This result is in agreement with recently published experimental data.
In this high-$x$ region, both the flavour content and structure of the nucleon parton distribution functions remains relatively poorly known. New LHCb measurements of Z and charm jet associated production could indicate a valence-like intrinsic-charm component in the proton wave function, and measurements of Z production in pPb collisions provide new constraints on the partonic structure of nucleons bound inside nuclei. Here we will discuss these new LHCb measurements and comparisons with state-of-the-art parton distribution function calculations.
Studies of fragmentation and parton density functions are a core component of researchin high energy particle and nuclear physics. These quantities are inherently interestingas a probe of the quantum nature of the strong force and are also essential ingredients toadditional studies in high energy scattering experiments. These proceedings provide anoverview of the state of the art in this area, as presented at the Deep-Inelastic ScatteringConference in the Spring of 2021.
The scale factor $σ_{eff}$, which characterizes double parton collisions in high energy hadron interactions, is a direct manifestation of the distribution of the interacting partons in transverse space, in such a way that different distributions give rise to different values of $σ_{eff}$ in different double parton collision processes. We work out the value of the scale factor in a few reactions of interest, in a correlated model of the multi-parton density of the proton recently proposed.
This paper gives a summary of selected highlights discussed in the working group on "Structure Functions and Parton Densities" (WG1) at the DIS 2017 conference. From the many talks presented we extract some general themes discussed with respect to global PDF fits, new PDF-sensitive measurements from the LHC experiments and elsewhere, exploitation of new ideas, tools to perform PDF fits, PDFs of heavy nuclei, and finally progress in basic theory calculations.
Partons are defined as the quanta in a Fock space description of a hadron. Gluon saturation is described in the Weizsäcker-Williams approximation for a large nucleus. The elements of DGLAP and BFKL evolution are given with the BFKL equation derived in a large-$N_c$ dipole formalism. A more general discussion of saturation is given in terms of a dipole scattering on a nucleon or nucleus. Possible evidence for saturation at HERA is discussed.
