Generalized Parton Distributions Research Articles

Multigrid multilevel Monte Carlo for a lattice with a displacement

AbstractThe Hutchinson method can be used to estimate the trace of a function of a matrix A, that is, , stochastically. With the variance of the Hutchinson estimator decreasing as , techniques to reduce the variance of this estimator become necessary due to the high accuracy required by some calculations in scientific computing. In lattice QCD, where A is the Dirac operator D stemming from a discretization of the Dirac equation, the accuracy of some calculations involving renders them practically unfeasible if one uses the Hutchinson estimator to approximate the trace. One such variance reduction technique, known as multigrid multilevel Monte Carlo, has been introduced recently to deal with for the Laplace 2D, Gauge Laplacian, and Schwinger problems. We use it here in the context of lattice QCD, and moreover, we analyze its impact when dealing with , where is the matrix that emerges when a displacement in one of the four spacetime dimensions of the lattice is introduced. This latter trace is of importance when computing generalized parton distributions in lattice QCD.

Predictions for exclusive varUpsilon photoproduction in ultraperipheral {textrm{Pb}}+{textrm{Pb}} collisions at the LHC at next-to-leading order in perturbative QCD

We present predictions for the rapidity-differential cross sections of exclusive varUpsilon photoproduction in ultraperipheral collisions (UPCs) of lead ions at the Large Hadron Collider (LHC). We work in the framework of collinear factorization at next-to-leading order (NLO) in perturbative QCD, modeling the generalized parton distributions (GPDs) through the Shuvaev transform of nuclear parton distribution functions (nPDFs). Our direct NLO predictions depend significantly on nPDF uncertainties and on the choices of the factorization and renormalization scales, but to a much lesser degree on GPD modeling. To tame the scale dependence and to account for the fact that the NLO calculations generally underpredict the photoproduction measurements on protons, we also present alternative, data-driven predictions. In this approach the underlying photoproduction cross sections on lead are found by combining their nuclear modifications calculated at NLO with the measured photoproduction cross sections on protons. The data-driven strategy reduces the uncertainties associated with the scale choices, and essentially eliminates the effects of GPD modeling thereby leaving the cross sections sensitive mainly to the input nPDFs. Our estimates indicate that the process is measurable in {textrm{Pb}}+{textrm{Pb}} collisions at the LHC.

First Measurement of Hard Exclusive π^{-}Δ^{++} Electroproduction Beam-Spin Asymmetries off the Proton.

The polarized cross-section ratio σ_{LT^{'}}/σ_{0} from hard exclusive π^{-}Δ^{++} electroproduction off an unpolarized hydrogen target has been extracted based on beam-spin asymmetry measurements using a 10.2 GeV/10.6 GeV incident electron beam and the CLAS12 spectrometer at Jefferson Lab. The study, which provides the first observation of this channel in the deep-inelastic regime, focuses on very forward-pion kinematics in the valence regime, and photon virtualities ranging from 1.5 GeV^{2} up to 7 GeV^{2}. The reaction provides a novel access to the d-quark content of the nucleon and to p→Δ^{++} transition generalized parton distributions. A comparison to existing results for hard exclusive π^{+}n and π^{0}p electroproduction is provided, which shows a clear impact of the excitation mechanism, encoded in transition generalized parton distributions, on the asymmetry.

Exclusive dilepton production in photon-induced interactions at RHIC

The exclusive dilepton photoproduction in pp and pAu collisions at RHIC is investigated considering the contribution of the Bethe–Heitler (BH) and the timelike Compton scattering (TCS) processes. The TCS amplitude is estimated at next-to-leading-order of the strong running coupling constant alpha _s and assuming the Goloskokov–Kroll model for the quark and gluon generalized parton distributions. The TCS differential cross section is estimated as well the contribution associated to the interference between the TCS and BH amplitudes. Predictions for the TCS, BH and interference contributions are presented considering the kinematical range covered by the RHIC detectors.

Exclusive meets inclusive particle production at small Bjorken xB : How to relate exclusive measurements to PDFs based on evolution equations

Exclusive heavy-vector-meson photoproduction is a prominent signal in collider experiments with hadron beams. At the highest photon-hadron collision energies, this process is considered as a candidate to constrain gluon parton distribution functions (PDFs) at small longitudinal momentum fractions. However, in the framework of collinear factorisation, exclusive particle production is described in terms of generalised parton distributions (GPDs). In this contribution, we investigate at the leading order in $\alpha_s$ the connection between GPDs and PDFs. Our main result is a proposal to quantify the systematic uncertainty inherent to this connection. We put our approach into context with respect to the Shuavev transform. Our uncertainty estimate can be straightforwardly adapted to higher fixed orders and small-$x$ resummations. The question of extrapolating GPDs to vanishing skewness is paramount for the programme of the Electron Ion Collider (EIC), notably for the extraction of the radial distributions of partons.

Generalized parton distributions of sea quark at zero skewness in the light-cone model

We study the chiral-even generalized parton distributions (GPDs) of {bar{u}} and {bar{d}} quarks at zero skewness using the overlap representation within the light cone formalism. The GPDs of {bar{u}} and {bar{d}} quarks can be expressed as the convolution of the light cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |q{bar{q}}Brangle Fock states. We present the numerical results for H^{{bar{u}}/P}(x,xi ,Delta ^2), H^{{bar{d}}/P}(x,xi ,Delta ^2), E^{{bar{u}}/P}(x,xi ,Delta ^2) and E^{{bar{d}}/P}(x,xi ,Delta ^2). We apply the model resulting GPDs to calculate the orbital angular momentum of the {bar{u}} and {bar{d}} quarks, showing that L^{{bar{u}}/P}, L^{{bar{d}}/P} are positive and L^{{bar{u}}/P} is smaller than L^{{bar{d}}/P}. The sea quark OAM distributions in the impact parameter space L_{{bar{q}}}(x,{varvec{b}}_{varvec{T}}) are also calculated.

Generalized Parton Distributions of Pions at the Forthcoming Electron-Ion Collider

Generalized Parton Distributions of Pions at the Forthcoming Electron-Ion Collider

Phenomenology of double deeply virtual Compton scattering in the era of new experiments

We revisit the phenomenology of the deep exclusive electroproduction of a lepton pair, i.e. double deeply virtual Compton scattering (DDVCS), in view of new experiments planned in the near future. The importance of DDVCS in the reconstruction of generalized parton distributions (GPDs) in their full kinematic domain is emphasized. Using Kleiss-Stirling spinor techniques, we provide the leading order complex amplitudes for both DDVCS and Bethe-Heithler sub-processes. Such a formulation turns out to be convenient for practical implementation in the PARTONS framework and EpIC Monte Carlo generator that we use in simulation studies.

Vector meson gravitational form factors and generalized parton distributions at finite temperature within the soft-wall AdS/QCD model

We investigate the vector meson’s gravitational form factors (GFFs) and generalized parton distributions (GPDs) at finite temperatures within the soft-wall AdS/ QCD model. The plotted soft-wall GFFs graphs at zero temperature are close to the hard-wall results (Abidin and Carlson in Phys. Rev. D 77:095007, arXiv:0801.3839 [hep-th], 2008). The dependence on temperature of the GFFs and GPDs is studied using the thermal dilaton approach in the soft-wall model. Plots of thermal GFFs show that they decrease in temperature increase. Also, the gravitational radius of rho meson decreases in temperature growth and becomes zero around the critical temperature T_c=0.2 mathrm{ GeV}. GPDs at zero skewness are plotted and analyzed at zero and finite temperature cases.

First CLAS12 Measurement of Deeply Virtual Compton Scattering Beam-Spin Asymmetries in the Extended Valence Region.

Deeply virtual Compton scattering (DVCS) allows one to probe generalized parton distributions describing the 3D structure of the nucleon. We report the first measurement of the DVCS beam-spin asymmetry using the CLAS12 spectrometer with a 10.2 and 10.6GeV electron beam scattering from unpolarized protons. The results greatly extend the Q^{2} and Bjorken-x phase space beyond the existing data in the valence region and provide 1600 new data points measured with unprecedented statistical uncertainty, setting new, tight constraints for future phenomenological studies.

Study of transversity GPDs from pseudoscalar mesons production at EIC of China

The exclusive η and π 0 electroproduction is studied in the handbag approach based on the generalized parton distributions (GPDs) factorization. Predictions of π 0 and η mesons are calculated for future electron-ion collider in China (EicC) energy ranges, using obtained cross sections we extract information on the transversity GPDs contributions to these processes.

Form factors of the nucleon by using the t dependence of parton distribution functions

This paper calculates the elastic form factors for nucleons based on generalized parton distributions using an extended new ansatz introduced in http://dx.doi.org/10.1103/PhysRevC.105.025202 (Phys. Rev. C 105, no.2, 025202 (2022)). Different parton distribution functions (PDFs) are considered, and modifications are made to the free parameters of the new ansatz. The obtained results are systematically compared among the combinations of different PDFs and ansatzes for high ranges of momentum transfer, with $-t < 35 GeV^{-2}$. The minimum suitable parameters are used to parametrize the model. After obtaining the form factors, we proceed to compute the electric radius and the transversely unpolarized densities for the nucleon. In addition, we derive the parton distribution functions (PDFs) that depend on the impact parameter. Finally, we analyze the results by comparing them with the findings from other research and experimental data.

Parton decomposition of nucleon spin and momentum: Gluons from dressed quarks

The lowest two Mellin moments of hadronic Generalized Parton Distributions are explored within a model that allows investigation of the inter-related quark and gluon contributions. For light quarks their dynamical connection is strong due to quark dressing. Our principal focus is the angular momentum J of the nucleon. This work employs and extends dynamical insights obtained from our recent model results for quark and gluon momentum fractions 〈x〉q/g in both pion and nucleon. The employed model is based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations of QCD. The special case of a 1-loop treatment of a single hadronic quark is used to motivate several insights and obtain initial estimates such as the Wilson line correction to the established Landau gauge model (−7% for both Jq and 〈x〉q), and the “binding gluon” contribution to 〈x〉g (≤10%). We obtain the proton J within 1% after inclusion of the pion cloud mechanism to produce the sea. The gluon second Mellin moments of the proton reflect similar dynamics; (〈x〉g, Jg) are (26%, 24%) at model scale, and (40%, 38%) at 2 GeV. We also find that Jtot is shared almost equally between the total orbital and total intrinsic spin contributions.

Generalized parton distributions through universal moment parameterization: non-zero skewness case

We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs) and deeply virtual Compton scattering (DVCS) measurements. Following the previous work where we parameterize GPDs in terms of their moments, we extend the framework to allow for the global analysis at non-zero skewness. Together with the constraints at zero skewness, we fit GPDs to global DVCS measurements from both the recent JLab and the earlier Hadron-Electron Ring Accelerator (HERA) experiments with two active quark flavors and leading order QCD evolution. With certain choices of empirical constraints, both sea and valence quark distributions are extracted with the combined inputs, and we present the quark distributions in the proton correspondingly. We also discuss how to extend the framework to accommodate more off-forward constraints beyond the small ξ expansion, especially the lattice calculated GPDs.

Generalized parton distributions at zero skewness

We present a new determination of the generalized parton distributions (GPDs) with their uncertainties at zero skewness, $ \xi =0 $, through a simultaneous analysis of all available experimental data of the nucleon electromagnetic form factors (FFs), nucleon charge and magnetic radii, proton axial FFs (AFFs) and wide-angle Compton scattering (WACS) cross sections for the first time, and we investigate whether there is any tension between these data. This can be considered the most comprehensive analysis of GPDs at $ \xi=0 $ performed so far. We show that such an analysis provides the simultaneous determination of three kinds of GPDs, namely $ H^q $, $ \widetilde{H}^q $ and $ E^q $, considering also the sea-quark contributions. As a result, we find that the inclusion of the WACS and AFF data at larger values of the momentum transfer squared $ Q^2=-t $ can put new constraints on GPDs and change them drastically in some cases. We show that there is a considerable tension between the WACS and the proton magnetic form factor ($ G_M^p $) data, especially at larger values of $ -t $. However, we indicate that the results for the gravitational FF $ M_2 $ and the proton total angular momentum $ J^p $ calculated using the extracted GPDs are in relatively good agreement with the light-cone QCD sum rules (LCSRs) and lattice QCD predictions when the sea-quark contributions are considered and both WACS and $ G_M^p $ data are included in the analyses simultaneously.

Hadronic structure on the light front. VI. Generalized parton distributions of unpolarized hadrons

We discuss the generalized parton distributions (GPDs) for unpolarized hadrons, as a continuation of our recent work on hadronic structure on the light front. We analyze the unpolarized GPDs for the light nucleon and delta, as well as generic mesons, using the lowest Fock states. We use these GPDs to reconstruct the charge and gravitational form factors, and discuss their relative sizes. The results are also compared to reported QCD lattice results.

Unpolarized generalized parton distributions of light and heavy vector mesons

We study the leading-twist unpolarized generalized parton distributions (GPDs) of light and heavy vector mesons, i.e., the $\ensuremath{\rho}$, $J/\ensuremath{\psi}$, and $\mathrm{\ensuremath{\Upsilon}}$, at zero skewness. An ansatz incorporating the zero-mode contribution is introduced to modify the light front overlap representation of GPDs. The leading Fock-state light front wave functions of vector mesons from Dyson-Schwinger and Bethe-Salpeter equations approach are then employed to study the meson GPDs. The light front spatial distribution of valence quarks within vector mesons is then studied with the impact parameter dependent GPD. We also investigate the electromagnetic and gravitational form factors, which are the first and second Mellin moments of the GPDs. The light-cone mass radius of $\ensuremath{\rho}$ is determined to be 0.30 fm, close to a recent Nambu-Jona-Lasinio model prediction of 0.32 fm. For $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}$, they are predicted to be 0.151 fm and 0.089 fm respectively.

Accessing chiral-even quark generalised parton distributions in the exclusive photoproduction of a γπ± pair with large invariant mass in both fixed-target and collider experiments

We compute the exclusive photoproduction of a γπ± pair using the collinear factorisation framework, in the kinematic regime where the pair has a large invariant mass and the meson has a sufficiently large transverse momentum to not resonate with the outgoing nucleon. This exclusive channel presents a new avenue for the investigation of GPDs. It is particularly interesting as the high centre of mass energies available at future experiments will allow the study of GPDs at small skewness ξ. We compute the scattering amplitude of the process, at leading twist and leading order in αs, which is used to estimate its cross-section and linear polarisation asymmetries with respect to the incoming photon, for JLab 12-GeV, COMPASS, future EIC and LHC (in ultra-peripheral collisions) kinematics. We find that the order of magnitude of estimates are sufficiently large for a dedicated experimental analysis to be performed, especially at JLab. We also compare the results from an asymptotic distribution amplitude (DA) to those using a recently proposed holographic DA.

Off-shell generalized parton distributions and form factors of the pion

Off-shell effects in generalized parton distributions (GPDs) of the pion, appearing, e.g., in the Sullivan process, are considered. Due to the lack of crossing symmetry, the moments of GPDs involve also odd powers of the skewness (longitudinal momentum transfer) parameter, which results in emergence of new off-shell form factors. With current-algebra techniques, we derive exact relations between the four off-shell gravitational form factors of the pion, in analogy to the electromagnetic case. Our results place stringent constraints on the off-shell GPDs of the pion. We provide an explicit realization in terms of a chiral quark model, where we show that the off-shell effects in GPDs are potentially significant in modeling physical processes and should not be neglected.

Polarized gluon distribution in the proton from holographic light-front QCD

We obtain the gluon parton distribution functions (PDFs) in the proton within the extended light-front holographic QCD framework, where the proton couples with the spin-two Pomeron in Anti-de Sitter space, together with constraints imposed by the Veneziano model. The gluon helicity asymmetry, after satisfying the perturbative QCD constraints at small and large longitudinal momentum regions, agrees with existing experimental measurements. The polarized gluon distribution is consistent with global analyses. We predict the gluon helicity contribution to the proton spin, $\Delta G=0.221^{+0.056}_{-0.044}$, close to the recent analysis with updated data sets and PHENIX measurement and the lattice QCD simulations. We subsequently present the unpolarized and polarized gluon generalized parton distributions in the proton.