Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO

Abstract

For the first time, we present a lattice QCD determination of Mellin moments of unpolarized generalized parton distributions (GPDs) of the proton from an analysis of the quasi-GPD matrix elements within the short-distance factorization framework. We perform our calculation on an $N_f$=2+1+1 twisted mass fermions ensemble with a clover improvement at lattice spacing $a=0.093$ fm and a pion mass of $m_{\pi }=260$ MeV. Focusing on the zero-skewness case, the iso-vector and iso-scalar quasi-GPDs are calculated from the ${\gamma }_0$ definition, as well as a recently proposed Lorentz-invariant definition. We utilize data on both symmetric and asymmetric kinematic frames, which allows us to obtain the Mellin moments for several values of the momentum transfer, $-t$, in the range 0.17 to $2.77{\mathrm{GeV}}^2$. We use the ratio scheme for GPDs, i.e. renormalization group invariant ratios with leading-twist factorization formula and perturbatively calculated matching coefficients up to the next-next-to-leading order (NNLO) to extract Mellin moments of GPDs, which are consistent with renormalization-group improved results. We compare our determination from quasi-GPDs with the results extracted using standard calculations of Mellin moments of local operators, specifically those related to the electromagnetic and gravitational form factors. We estimated the moments of GPDs up to the fifth ones for the first time. By extrapolating the Mellin moments to $-t=0$, we obtained the quark charges, momentum fraction, as well as the angular momentum contributions to the proton spin. The impact parameter space interpretation of the GPD moments is discussed, which provides insights into the spatial distribution of unpolarized quarks and their correlations in the transverse plane of an unpolarized or transversely polarized proton.

arXiv comment28 pages, 22 figures

References in corpus (124)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
• Hard Exclusive Reactions and the Structure of Hadrons
• Parton Physics on Euclidean Lattice
• Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\zeta \to 0$
• Scaling Limit of Deeply Virtual Compton Scattering
• Impact Parameter Space Interpretation for Generalized Parton Distributions
• Generalized parton distributions and strong forces inside nucleons and nuclei
• Generalized parton distributions in impact parameter space
• Forces inside hadrons: pressure, surface tension, mechanical radius, and all that
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Nucleon Generalized Parton Distributions from Full Lattice QCD
• Relations between generalized and transverse momentum dependent parton distributions
• Nucleon Form Factors from Generalized Parton Distributions
• Large-Momentum Effective Theory
• Femto-Photography of Protons to Nuclei with Deeply Virtual Compton Scattering
• Nucleon Helicity and Transversity Parton Distributions from Lattice QCD
• Flavor Structure of the Nucleon Sea from Lattice QCD
• GPD phenomenology and DVCS fitting - Entering the high-precision era
• Extracting Parton Distribution Functions from Lattice QCD Calculations
• Novel quark smearing for hadrons with high momenta in lattice QCD
• Nucleon structure functions from lattice operator product expansion
• Moments of Nucleon Generalized Parton Distributions in Lattice QCD
• Deeply virtual Compton scattering at small x_B and the access to the GPD H
• A Lattice Calculation of Parton Distributions
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
• A complete non-perturbative renormalization prescription for quasi-PDFs
• Origin of Difference between $\overline{d}$ and $\overline{u}$ Partons in the Nucleon
• Vector meson electroproduction at small Bjorken-x and generalized parton distributions
• Perturbative Renormalization of quasi-PDFs
• On the Renormalizability of Quasi Parton Distribution Functions
• Deep-inelastic scattering and the operator product expansion in lattice QCD
• Renormalization in Large Momentum Effective Theory of Parton Physics
• Pion Distribution Amplitude from Lattice QCD
• Extraction of the proton radius from electron-proton scattering data
• Reconstruction of light-cone parton distribution functions from lattice QCD simulations at the physical point
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field
• Transverse spin structure of the nucleon from lattice QCD simulations
• Parton Distribution Function with Non-perturbative Renormalization from Lattice QCD
• Transverse Deformation of Parton Distributions and Transversity Decomposition of Angular Momentum
• Pion Valence Structure from Ioffe Time Pseudo-Distributions
• Transversity parton distribution functions from lattice QCD
• Updated Lattice Results for Parton Distributions
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Valence parton distribution function of pion from fine lattice
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• Nucleon form factors and moments of generalized parton distributions using $N_f=2+1+1$ twisted mass fermions
• Axial Vector Form Factors of the Nucleon from Lattice QCD
• Collins-Soper Kernel for TMD Evolution from Lattice QCD
• Proton and neutron electromagnetic form factors from lattice QCD
• Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
• Ioffe-time distributions instead of parton momentum distributions in description of deep inelastic scattering
• Nucleon axial form factors using lattice QCD simulations with a physical value of the pion mass
• Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Chromodynamic Lensing and Transverse Single Spin Asymmetries
• Simulating twisted mass fermions at physical light, strange and charm quark masses
• Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum Effective Theory
• Flexible Parametrization of Generalized Parton Distributions from Deeply Virtual Compton Scattering Observables
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
• Pion generalized parton distribution from lattice QCD
• Double deeply virtual Compton scattering off the nucleon
• Complex conformal spin partial wave expansion of generalized parton distributions and distribution amplitudes
• Improved Parton Distribution Functions at Physical Pion Mass
• Parton Distribution Functions from Ioffe time pseudo-distributions
• Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass
• Pion and Kaon Distribution Amplitudes from Lattice QCD
• Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point
• Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching
• Valence-Quark Distribution of the Kaon and Pion from Lattice QCD
• Nonperturbative Determination of Collins-Soper Kernel from Quasi Transverse-Momentum Dependent Wave Functions
• Lattice QCD calculation of the Collins-Soper kernel from quasi TMDPDFs
• Iso-vector axial form factors of the nucleon in two-flavour lattice QCD
• Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Exclusive electroproduction of lepton pairs as a probe of nucleon structure
• Pion and Kaon Distribution Amplitudes in the Continuum Limit
• Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions
• Nucleon electromagnetic form factors in twisted mass lattice QCD
• The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD
• Matching Quasi Generalized Parton Distributions in the RI/MOM scheme
• Determination of the Collins-Soper Kernel from Lattice QCD
• Lattice QCD Study of Transverse-Momentum Dependent Soft Function
• The deconvolution problem of deeply virtual Compton scattering
• Moments of nucleon generalized parton distributions from lattice QCD
• Isovector parton distribution functions of the proton on a superfine lattice
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks
• Interpretation of the Flavor Dependence of Nucleon Form Factors in a Generalized Parton Distribution Model
• Nucleon electromagnetic form factors using lattice simulations at the physical point
• Extraction of Next-to-Next-to-Leading-Order PDFs from Lattice QCD Calculations
• Continuum-extrapolated NNLO Valence PDF of Pion at the Physical Point
• Lattice QCD Determination of the Bjorken-$x$ Dependence of Parton Distribution Functions at Next-to-next-to-leading Order
• Model independent determination of the light-cone wave functions for exclusive processes
• Single diffractive hard exclusive processes for the study of generalized parton distributions
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Computing the nucleon charge and axial radii directly at $Q^2=0$ in lattice QCD
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Parton distribution functions of ${\Delta }^{+}$ on the lattice
• Hard photoproduction of a diphoton with a large invariant mass
• Distribution Amplitudes of $K^{\ast }$ and $\varphi$ at Physical Pion Mass from Lattice QCD
• Lattice continuum-limit study of nucleon quasi-PDFs
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• Next-to-next-to-leading order corrections to quark Quasi parton distribution functions
• Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions
• Nucleon generalized form factors from two-flavor lattice QCD
• Generalized Parton Distributions: visions, basics, and realities
• Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs
• Generalized parton distributions through universal moment parameterization: zero skewness case
• The role of zero-mode contributions in the matching for the twist-3 PDFs $e(x)$ and $h_L(x)$
• Flavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
• Flavor decomposition for the proton helicity parton distribution functions
• Generalized parton distributions through universal moment parameterization: non-zero skewness case
• One-loop matching for the twist-3 parton distribution $g_T(x)$
• Probing axial quark generalized parton distributions through exclusive photoproduction of a $\gamma {\pi }^{\pm }$ pair with a large invariant mass
• Parton physics from a heavy-quark operator product expansion: Formalism and Wilson coefficients
• First moments of the nucleon transverse quark spin densities using lattice QCD
• Parton distribution functions beyond leading twist from lattice QCD: The $h_L(x)$ case
• Generalized parton distributions at zero skewness
• Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections
• Generalised parton distributions from the off-forward Compton amplitude in lattice QCD
• Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude
• Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs

Cited by in corpus (15)

• Updated analysis of near-threshold heavy quarkonium production for probe of proton's gluonic gravitational form factors
• Towards Unpolarized GPDs from Pseudo-Distributions
• QCD Predictions for Meson Electromagnetic Form Factors at High Momenta: Testing Factorization in Exclusive Processes
• Moments of Axial-Vector GPD from Lattice QCD: Quark Helicity, Orbital Angular Momentum, and Spin-Orbit Correlation
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Impact of JLab data on the determination of GPDs at zero skewness and new insights from transition form factors $N\to \Delta$
• Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions
• Parametrization of GPDs from t-channel string exchange in AdS spaces
• String-based parametrization of nucleon GPDs at any skewness: a comparison to lattice QCD
• Exploring Baryon Resonances with Transition Generalized Parton Distributions: Status and Perspectives
• Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
• String-based axial and helicity-flip GPDs: a comparison to lattice QCD
• Systematic description of hadron's response to non-local QCD probes: Froissart-Gribov projections in analysis of deeply virtual Compton scattering
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem