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Parton distributions and lattice-QCD calculations: Toward 3D structure

Journal Article · · Prog.Part.Nucl.Phys.

The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

Research Organization:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
DOE Contract Number:
AC02-07CH11359
OSTI ID:
1843473
Report Number(s):
Nikhef 2020-018; MIT-CTP/5213; MSUHEP-20-012; IFJPAN-IV-2020-3; SMU-HEP-20-03; DESY-20-109; FERMILAB-PUB-20-787-SCD; arXiv:2006.08636; oai:inspirehep.net:1801417
Journal Information:
Prog.Part.Nucl.Phys., Vol. 121
Country of Publication:
United States
Language:
English

References (247)

Parton distributions and lattice QCD calculations: A community white paper journal May 2018
Factorization Of Hard Processes In QCD book July 1989
Asymptotic freedom in parton language journal August 1977
The structure of the proton in the LHC precision era journal May 2018
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results journal June 2019
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all journal September 2016
LHC Machine journal August 2008
Parton distributions in the LHC era: MMHT 2014 PDFs journal May 2015
The impact of the final HERA combined data on PDFs obtained from a global fit journal April 2016
The impact of LHC jet data on the MMHT PDF fit at NNLO journal March 2018
Differential top quark pair production at the LHC: Challenges for PDF fits journal January 2020
Parton distributions from high-precision collider data: NNPDF Collaboration journal October 2017
Direct photon production and PDF fits reloaded journal June 2018
Parton distributions with theory uncertainties: general formalism and first phenomenological studies: NNPDF Collaboration journal November 2019
Nuclear uncertainties in the determination of proton PDFs: NNPDF Collaboration journal March 2019
A critical appraisal and evaluation of modern PDFs journal August 2016
The ABM parton distributions tuned to LHC data journal March 2014
Delineating parton distributions and the strong coupling journal April 2014
Combination of measurements of inclusive deep inelastic $${e^{\pm }p}$$ e ± p scattering cross sections and QCD analysis of HERA data: H1 and ZEUS Collaborations journal December 2015
Precision measurement and interpretation of inclusive $$W^+$$ W + , $$W^-$$ W - and $$Z/\gamma ^*$$ Z / γ ∗ production cross sections with the ATLAS detector journal June 2017
QCD analysis of the ATLAS and CMS W ± and Z cross-section measurements and implications for the strange sea density journal July 2018
Measurements of top-quark pair differential cross-sections in the lepton+jets channel in pp collisions at $$\sqrt{s}=8\,~{\mathrm {TeV}}$$ s = 8 TeV using the ATLAS detector journal October 2016
Measurement of top quark pair differential cross sections in the dilepton channel in p p collisions at s = 7 and 8 TeV with ATLAS journal November 2016
Measurement of the differential cross section and charge asymmetry for inclusive $$\mathrm {p}\mathrm {p}\rightarrow \mathrm {W}^{\pm }+X$$ p p → W ± + X production at $${\sqrt{s}} = 8$$ s = 8 TeV journal August 2016
Small-x resummation from HELL journal November 2016
Towards parton distribution functions with small-x resummation: HELL 2.0 journal December 2017
Impact of low-x resummation on QCD analysis of HERA data journal August 2018
Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data journal April 2018
Operator expansion for high-energy scattering journal March 1996
The BFKL equation from the Wilson renormalization group journal October 1997
Universal features of JIMWLK and BK evolution at small x journal July 2004
Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV journal June 2019
Gluon Shadowing in Heavy-Flavor Production at the LHC journal August 2018
Vector boson production in pPb and PbPb collisions at the LHC and its impact on nCTEQ15 PDFs journal July 2017
EPPS16: nuclear parton distributions with LHC data journal March 2017
Global analysis of nuclear parton distribution functions and their uncertainties at next-to-next-to-leading order journal January 2016
The g1 problem: Deep inelastic electron scattering and the spin of the proton journal June 1990
A first unbiased global determination of polarized PDFs and their uncertainties journal October 2014
New analysis concerning the strange quark polarization puzzle journal March 2015
First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis journal September 2017
Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation journal May 2018
Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach journal June 2016
Order-αs2 corrections to the polarized structure function g1 (x, Q2) journal April 1994
Towards semi-inclusive deep inelastic scattering at next-to-next-to-leading order journal February 2017
Jet Production in Polarized Deep Inelastic Scattering at Next-to-Next-to-Leading Order journal August 2020
Flavor structure of the nucleon sea journal November 2014
Small- and large- x nucleon spin structure from a global QCD analysis of polarized parton distribution functions journal March 2015
Polarized ρ mesons and the asymmetry between and in the sea of the nucleon journal December 1998
On the polarization of the nucleon sea in the meson-cloud model journal August 1999
The flavor asymmetry of polarized anti-quarks in the nucleon journal June 2001
Polarized light-antiquark distributions in a meson-cloud model journal January 2002
Polarized parton distributions at an electron–ion collider journal January 2014
Chiral-odd parton distributions and polarized Drell-Yan process journal July 1991
Fragmentation of transversely polarized quarks probed in transverse momentum distributions journal May 1993
Transverse spin-dependent azimuthal correlations of charged pion pairs measured in p ↑  +  p collisions at s = 500  GeV journal May 2018
Collins azimuthal asymmetries of hadron production inside jets journal November 2017
Interference Fragmentation Functions and the Nucleon's Transversity journal February 1998
Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering journal June 2012
A high-statistics measurement of transverse spin effects in dihadron production from muon–proton semi-inclusive deep-inelastic scattering journal September 2014
Observation of Transverse Polarization Asymmetries of Charged Pion Pairs in e + e − Annihilation near s = 10.58     GeV journal August 2011
First extraction of valence transversities in a collinear framework journal March 2013
Improved extraction of valence transversity distributions from inclusive dihadron production journal May 2015
First Extraction of Transversity from a Global Analysis of Electron-Proton and Proton-Proton Data journal May 2018
Positivity Constraints for Spin-Dependent Parton Distributions journal February 1995
Parton distributions for the LHC journal July 2009
A constrained fit of the valence transversity distributions from dihadron production journal May 2020
Origin of difference between u ¯ and d ¯ partons in the nucleon journal March 1994
Exclusive processes in position space and the pion distribution amplitude journal May 2008
Parton physics from large-momentum effective field theory journal May 2014
Nonperturbative evolution of parton quasi-distributions journal April 2017
Nucleon Structure Functions from Operator Product Expansion on the Lattice journal June 2017
QCD Factorization and PDFs from Lattice QCD Calculation journal January 2015
Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations journal January 2018
Frontiers in lattice nucleon structure journal April 2020
Hadrons and nuclei journal November 2019
Recent Progress on Nucleon Structure with Lattice qcd journal January 2014
Nucleon helicity and transversity parton distributions from lattice QCD journal October 2016
Improved quasi parton distribution through Wilson line renormalization journal February 2017
Renormalization in Large Momentum Effective Theory of Parton Physics journal March 2018
More on large-momentum effective theory approach to parton physics journal November 2017
One-loop matching for parton distributions: Nonsinglet case journal July 2014
Matching the quasiparton distribution in a momentum subtraction scheme journal March 2018
A complete non-perturbative renormalization prescription for quasi-PDFs journal October 2017
Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass journal December 2018
Light-Cone Parton Distribution Functions from Lattice QCD journal September 2018
Pion distribution amplitude from Euclidean correlation functions journal March 2018
Model independent determination of the light-cone wave functions for exclusive processes journal November 1998
Quark pseudodistributions at short distances journal June 2018
Structure of parton quasi-distributions and their moments journal January 2019
Space-time picture of photon and neutrino scattering and electroproduction cross section asymptotics journal September 1969
Parton distribution functions from Ioffe time pseudo-distributions journal December 2019
Metallic microwave dielectric response of polyacetylene journal September 1995
Moments of Ioffe time parton distribution functions from non-local matrix elements journal November 2018
Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks journal April 2019
Evolution equations for QCD string operators journal January 1989
Positron-annihilation studies of quasicrystalline-phase Al-Mn-Si-Ru and α-phase alloys journal February 1994
Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks journal December 1977
Gluon Quasi-Parton-Distribution Functions from Lattice QCD journal December 2018
The theory of deeply inelastic scattering journal March 2013
Lattice calculation of hadronic tensor of the nucleon journal January 2018
Towards the nucleon hadronic tensor from lattice QCD journal June 2020
Parton degrees of freedom in PDFs from the hadronic tensor and large momentum effective theory journal October 2020
The Resolving Power of Gross Earth Data journal October 1968
Maximum entropy analysis of the spectral functions in lattice QCD journal January 2001
Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories journal October 2013
Quarkonium in-medium properties from realistic lattice NRQCD journal November 2018
Electron Spin Waves in Nonmagnetic Conductors: Self-Consistent-Field Theory journal April 1971
FLAG Review 2019: Flavour Lattice Averaging Group (FLAG) journal February 2020
Proton Mass Decomposition from the QCD Energy Momentum Tensor journal November 2018
Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities journal August 1966
Inelastic Scattering of Polarized Leptons from Polarized Nucleons journal March 1970
A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics journal May 2018
Quark contribution to the proton spin from 2 + 1 + 1 -flavor lattice QCD journal November 2018
The neutron and its role in cosmology and particle physics journal October 2011
Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation journal March 2017
Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology journal October 2015
Nucleon isovector tensor charge from lattice QCD using chiral fermions journal May 2020
Parton distributions from lattice data: the nonsinglet case journal October 2019
Measurement of the production of a W boson in association with a charm quark in pp collisions at $ \sqrt{s} $ = 7 TeV with the ATLAS detector journal May 2014
The strangest proton? journal December 2020
A general method for non-perturbative renormalization of lattice operators journal July 1995
Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD journal January 1994
Gauge-Invariant Decomposition of Nucleon Spin journal January 1997
Scaling limit of deeply virtual compton scattering journal July 1996
Generalized parton distributions and strong forces inside nucleons and nuclei journal February 2003
Generalized parton distributions journal December 2003
Generalized Parton Distributions journal December 2004
Unraveling hadron structure with generalized parton distributions journal October 2005
GPD phenomenology and DVCS fitting: Entering the high-precision era journal June 2016
Impact Parameter Space Interpretation for Generalized Parton Distributions journal January 2003
Transverse deformation of parton distributions and transversity decomposition of angular momentum journal November 2005
Deeply virtual Compton scattering journal June 1997
Hard exclusive reactions and the structure of hadrons journal January 2001
Concurrent approaches to Generalized Parton Distribution modeling: the pion’s case journal January 2017
PARTONS: PARtonic Tomography Of Nucleon Software: A computing framework for the phenomenology of Generalized Parton Distributions journal June 2018
Towards a fitting procedure to deeply virtual meson production – the next-to-leading order case journal July 2014
Description and interpretation of DVCS measurements journal January 2016
The role of the quark and gluon GPDs in hard vector-meson electroproduction journal November 2007
Kinematically complete experiment on transfer excitation in intermediate-energy p + He collisions journal September 2006
Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer journal November 1999
First measurement of the electric formfactor of the neutron in the exclusive quasielastic scattering of polarized electrons from polarized 3He journal May 1994
Charge Form Factor of the Neutron from the Reaction 2 H → ( e → , e ′ n ) p journal June 1999
Measurements of G E n / G M n from the H 2 ( e → , e ′ n → ) H 1 Reaction to Q 2 = 1.45 ( G e V / c ) 2 journal September 2003
Measurement of the Neutron Electric Form Factor G en at 0.67 ( GeV / c ) 2 via 3 He → ( e → , e ′ n ) journal November 1999
The neutron charge form factor and target analyzing powers from 3He(e→,e′n) scattering journal July 2003
Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆ journal January 2005
Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding journal June 1999
Measurement of the Neutron Electric Form Factor G E , n in the Quasifree H 2 ( e → , e ′ n → ) p Reaction journal July 1999
Precision measurement of the neutron magnetic form factor journal September 1994
Precise measurements of the neutron magnetic form factor journal June 1998
Precise neutron magnetic form factors journal January 2002
Nucleon form factors and the BLAST experiment journal June 2007
Nucleon strangeness form factors from N f = 2 + 1 clover fermion lattice QCD journal November 2009
Exploring strange nucleon form factors on the lattice journal March 2012
Strange Quark Magnetic Moment of the Nucleon at the Physical Point journal January 2017
Strange Electromagnetic Form Factors of the Nucleon with N f = 2 + 1 O ( a ) -Improved Wilson Fermions journal November 2019
Isovector axial form factors of the nucleon in two-flavor lattice QCD journal January 2019
Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors journal February 2019
Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG) journal February 2017
Vector and axial nucleon form factors: A duality constrained parameterization journal December 2007
Nucleon axial radius and muonic hydrogen—a new analysis and review journal July 2018
Proton Spin Structure from Measurable Parton Distributions journal October 2012
Generalized quasi parton distributions in a diquark spectator model journal January 2019
Unpolarized and Helicity Generalized Parton Distributions of the Proton within Lattice QCD journal December 2020
Border and skewness functions from a leading order fit to DVCS data journal November 2018
Unbiased determination of DVCS Compton form factors journal July 2019
Data-driven study of timelike Compton scattering journal February 2020
HERMES impact for the access of Compton form factors journal July 2014
The pressure distribution inside the proton journal May 2018
Measurability of pressure inside the proton journal June 2019
Covariant extension of the GPD overlap representation at low Fock states journal December 2017
Timelike Compton scattering: exclusive photoproduction of lepton pairs journal April 2002
Timelike Compton scattering off the proton and generalized parton distributions journal August 2015
Orbital and magnetic orderings in localized t 2 g systems, YTiO 3 and YVO 3 : Comparison with a more itinerant e g system LaMnO 3 journal September 1998
Transversity in hard exclusive electroproduction of pseudoscalar mesons journal September 2011
Rosenbluth Separation of the π 0 Electroproduction Cross Section journal December 2016
A glimpse of gluons through deeply virtual compton scattering on the proton journal November 2017
Transverse momentum distribution in Drell-Yan pair and W and Z boson production journal January 1985
Effect of a Transverse Momentum Distribution in the Parton Model journal November 1970
Galilean invariance in the infinite momentum frame and the parton model journal October 1971
Parton model and the Bethe-Salpeter wave function journal February 1977
Intrinsic transverse momentum: Nongauge theories journal May 1980
Parton distribution and decay functions journal January 1982
Back-to-back jets in QCD journal December 1981
Measurement of Asymmetries of Inclusive Pion Production in Proton-Proton Interactions at 6 and 11.8 GeV/ c journal April 1976
Asymmetries in inclusive proton-nucleon scattering at 11.75 GeV/ c journal December 1978
Spin dependence of the inclusive reaction p + p (polarized) → π0 + X at 24 GeV/c for high-pT π0 produced in the central region journal August 1980
Observation of significant spin effects in hard collisions at 40 GeV/c journal July 1990
Single-spin asymmetry in inclusive reactions p ↑ +p→ π + +X, π − +X, and p+X at 13.3 and 18.5 GeV/ c journal February 1990
Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons journal May 1991
Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam journal August 1991
Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering journal March 2002
Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering journal May 2002
Final state interactions and gauge invariant parton distributions journal April 2003
Universality of T-odd effects in single spin and azimuthal asymmetries journal September 2003
QCD factorization for spin-dependent cross sections in DIS and Drell–Yan processes at low transverse momentum journal September 2004
The construction of gauge-links in arbitrary hard processes journal May 2006
Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis journal October 2008
The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal February 1996
Investigations into the flavor dependence of partonic transverse momentum journal November 2013
Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities journal April 2014
Study of the sign change of the Sivers function from STAR collaboration W/Z production data journal April 2017
Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production journal June 2017
Analysis of vector boson production within TMD factorization journal January 2018
Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production journal June 2019
Transverse Momentum Dependent (TMD) Parton Distribution Functions: Status and Prospects journal January 2015
The Color Glass Condensate journal November 2010
Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions journal September 2015
Interplay of the CGC and TMD frameworks to all orders in kinematic twist journal May 2019
Collinear and TMD quark and gluon densities from parton branching solution of QCD evolution equations journal January 2018
An overview of transverse-momentum-dependent factorization and evolution journal June 2016
Introduction to GPDs and TMDs journal June 2016
Drell–Yan production at small q T , transverse parton distributions and the collinear anomaly journal June 2011
Soft and collinear factorization and transverse momentum dependent parton distribution functions journal November 2013
A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory journal May 2012
An exponential regulator for rapidity divergences journal November 2020
Scheme dependence and transverse momentum distribution interpretation of Collins–Soper–Sterman resummation journal November 2015
Back-to-back jets: Fourier transform from b to kT journal April 1982
Breakdown of dimensional regularization in the Sudakov problem journal November 1992
Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone journal July 2012
Towards quasi-transverse momentum dependent PDFs computable on the lattice journal September 2019
Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation journal January 2017
Correspondence between Soft and Rapidity Anomalous Dimensions journal February 2017
Non-universality of transverse momentum dependent parton distribution functions journal May 2008
Semi-inclusive deep inelastic scattering at small transverse momentum journal February 2007
Full transverse-momentum spectra of low-mass Drell–Yan pairs at LHC energies journal August 2003
Intrinsic quark transverse momentum in the nucleon from lattice QCD journal December 2009
NMR study on the stability of the magnetic ground state in MnCr 2 O 4 journal September 2010
Notes on the orbital angular momentum of quarks in the nucleon journal February 2012
Liquid-crystalline properties and reentrance phenomena in PBLG solutions journal March 1980
QCD Prediction for Heavy Boson Transverse Momentum Distributions journal March 2001
Drell-Yan cross sections at small transverse momentum journal January 1985
Semi-inclusive deeply inelastic scattering at small q T journal August 1996
Nonperturbative functions for SIDIS and Drell–Yan processes journal April 2018
Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production journal November 2014
Effect of flavor-dependent partonic transverse momentum on the determination of the W boson mass in hadronic collisions journal January 2019
Measurement of the Transverse Single-Spin Asymmetry in p ↑ + p → W ± / Z 0 at RHIC journal April 2016
First Measurement of Transverse-Spin-Dependent Azimuthal Asymmetries in the Drell-Yan Process journal September 2017
Calculation of Transverse-Momentum-Dependent Evolution for Sivers Transverse Single Spin Asymmetry Measurements journal June 2012
TMD evolution of the Sivers asymmetry journal September 2013
Accessing the Transverse Dynamics and Polarization of Gluons inside the Proton at the LHC journal May 2014
Asymmetries in heavy quark pair and dijet production at an EIC journal August 2016
Single-spin asymmetries in $$p^\uparrow p \rightarrow J/\psi +X$$p↑p→J/ψ+X within a TMD approach: role of the color octet mechanism journal December 2019
Transverse-momentum-dependent gluon distribution functions in a spectator model journal August 2020
$$J/\psi $$ J / ψ production in polarized and unpolarized ep collision and Sivers and $$\cos 2\phi $$ cos 2 ϕ asymmetries journal December 2017
Quantum Brownian magneto-oscillator: Role of environmental spectrum and external magnetic field in decoherence and decay processes journal July 2015
Gluon TMDs and NRQCD matrix elements in $${J}{/}{\psi }$$J/ψ production at an EIC journal January 2020

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