Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum

doi:https://doi.org/10.1103/PhysRevD.98.074022

Title: Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum

Abstract

We derive new Lorentz invariance and equation of motion relations between twist-three generalized parton distributions (GPDs) and moments in the parton transverse momentum, k _T, of twist-two generalized transverse momentum-dependent distributions (GTMDs), as a function of the parton longitudinal momentum fraction x. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible equation of motion relations that can be written in the T-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the g ₂ structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.

Authors:: Rajan, Abha; Engelhardt, Michael; Liuti, Simonetta

Publication Date:: 2018-10-23

Research Org.:: New Mexico State Univ., Las Cruces, NM (United States); Univ. of Virginia, Charlottesville, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1478612

Alternate Identifier(s):: OSTI ID: 1610315

Grant/Contract Number:: SC0016286; FG02-96ER40965

Resource Type:: Journal Article: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; astronomy & astrophysics; physics; particle interactions; quantum chromodynamics; strong interaction

Citation Formats


                    Rajan, Abha, Engelhardt, Michael, and Liuti, Simonetta. Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum.  United States: N. p., 2018. 
        Web.  doi:10.1103/PhysRevD.98.074022.

Copy to clipboard


                    Rajan, Abha, Engelhardt, Michael, & Liuti, Simonetta. Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum.  United States.  https://doi.org/10.1103/PhysRevD.98.074022

Copy to clipboard


                    Rajan, Abha, Engelhardt, Michael, and Liuti, Simonetta. Tue .  
        "Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum".  United States.  https://doi.org/10.1103/PhysRevD.98.074022.

Copy to clipboard


                    
@article{osti_1478612,

  title        = {Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum},

  author       = {Rajan, Abha and Engelhardt, Michael and Liuti, Simonetta},

  abstractNote = {We derive new Lorentz invariance and equation of motion relations between twist-three generalized parton distributions (GPDs) and moments in the parton transverse momentum, kT, of twist-two generalized transverse momentum-dependent distributions (GTMDs), as a function of the parton longitudinal momentum fraction x. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible equation of motion relations that can be written in the T-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the g2 structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.},

  doi          = {10.1103/PhysRevD.98.074022},

  url          = {https://www.osti.gov/biblio/1478612},
  journal      = {Physical Review D},

  issn         = {2470-0010},

  number       = 7,

  volume       = 98,

  place        = {United States},

  year         = {2018},

  month        = {10}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record at https://doi.org/10.1103/PhysRevD.98.074022

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

GPD phenomenology and DVCS fitting: Entering the high-precision era
journal, June 2016

Kumerički, Krešimir; Liuti, Simonetta; Moutarde, Hervé
The European Physical Journal A, Vol. 52, Issue 6
https://doi.org/10.1140/epja/i2016-16157-3

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

Mulders, P. J.; Tangerman, R. D.
Nuclear Physics B, Vol. 461, Issue 1-2
https://doi.org/10.1016/0550-3213(95)00632-X

Color, Spin, and Flavor-Dependent Forces in Quantum Chromodynamics
conference, November 2011

Jaffe, R. L.
The Gregory Breit Centennial Symposium
https://doi.org/10.1142/9789812811530_0011

Deeply virtual Compton scattering amplitude in the parton model
journal, October 2000

Penttinen, M.; Polyakov, M. V.; Shuvaev, A. G.
Physics Letters B, Vol. 491, Issue 1-2
https://doi.org/10.1016/S0370-2693(00)01035-2

Measurements of $d_{2}^{n}$ and $A_{1}^{n}$ : Probing the neutron spin structure
journal, September 2016

Flay, D.; Posik, M.; Parno, D. S.
Physical Review D, Vol. 94, Issue 5
https://doi.org/10.1103/PhysRevD.94.052003

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables
journal, March 2016

Kanazawa, Koichi; Koike, Yuji; Metz, Andreas
Physical Review D, Vol. 93, Issue 5
https://doi.org/10.1103/PhysRevD.93.054024

Wigner, Husimi, and generalized transverse momentum dependent distributions in the color glass condensate
journal, November 2016

Hagiwara, Yoshikazu; Hatta, Yoshitaka; Ueda, Takahiro
Physical Review D, Vol. 94, Issue 9
https://doi.org/10.1103/PhysRevD.94.094036

Lorentz invariance relations among parton distributions revisited
journal, August 2003

Goeke, K.; Metz, A.; Pobylitsa, P. V.
Physics Letters B, Vol. 567, Issue 1-2
https://doi.org/10.1016/S0370-2693(03)00870-0

Power corrections at short distances
journal, January 1980

David Politzer, H.
Nuclear Physics B, Vol. 172
https://doi.org/10.1016/0550-3213(80)90172-8

Sivers and Boer-Mulders observables from lattice QCD
journal, May 2012

Musch, B. U.; Hägler, Ph.; Engelhardt, M.
Physical Review D, Vol. 85, Issue 9
https://doi.org/10.1103/PhysRevD.85.094510

Proton Spin Structure from Measurable Parton Distributions
journal, October 2012

Ji, Xiangdong; Xiong, Xiaonu; Yuan, Feng
Physical Review Letters, Vol. 109, Issue 15
https://doi.org/10.1103/PhysRevLett.109.152005

Deeply virtual Compton scattering
journal, June 1997

Ji, Xiangdong
Physical Review D, Vol. 55, Issue 11
https://doi.org/10.1103/PhysRevD.55.7114

Genuine twist-3 contributions to the generalized parton distributionsfrom instantons
journal, September 2004

Kiptily, D. V.; Polyakov, M. V.
The European Physical Journal C, Vol. 37, Issue 1
https://doi.org/10.1140/epjc/s2004-01957-3

Lattice QCD study of the Boer-Mulders effect in a pion
journal, March 2016

Engelhardt, M.; Hägler, P.; Musch, B.
Physical Review D, Vol. 93, Issue 5
https://doi.org/10.1103/PhysRevD.93.054501

Quark orbital dynamics in the proton from lattice QCD: From Ji to Jaffe-Manohar orbital angular momentum
journal, May 2017

Engelhardt, M.
Physical Review D, Vol. 95, Issue 9
https://doi.org/10.1103/PhysRevD.95.094505

Parameterization of the quark–quark correlator of a spin-<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> hadron
journal, July 2005

Goeke, K.; Metz, A.; Schlegel, M.
Physics Letters B, Vol. 618, Issue 1-4
https://doi.org/10.1016/j.physletb.2005.05.037

Generalized parton correlation functions for a spin-1/2 hadron
journal, August 2009

Meißner, Stephan; Metz, Andreas; Schlegel, Marc
Journal of High Energy Physics, Vol. 2009, Issue 08
https://doi.org/10.1088/1126-6708/2009/08/056

Twist analysis of the nucleon spin in QCD
journal, October 2012

Hatta, Yoshitaka; Yoshida, Shinsuke
Journal of High Energy Physics, Vol. 2012, Issue 10
https://doi.org/10.1007/JHEP10(2012)080

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects
journal, November 2017

Yoon, Boram; Engelhardt, Michael; Gupta, Rajan
Physical Review D, Vol. 96, Issue 9
https://doi.org/10.1103/PhysRevD.96.094508

Generalized parton distributions
journal, December 2003

Diehl, M.
Physics Reports, Vol. 388, Issue 2-4
https://doi.org/10.1016/j.physrep.2003.08.002

Two-hadron semi-inclusive production including subleading twist contributions
journal, April 2004

Bacchetta, Alessandro; Radici, Marco
Physical Review D, Vol. 69, Issue 7
https://doi.org/10.1103/PhysRevD.69.074026

Exact sum rule for transversely polarized DIS
journal, April 1997

Efremov, A. V.; Teryaev, O. V.; Leader, Elliot
Physical Review D, Vol. 55, Issue 7
https://doi.org/10.1103/PhysRevD.55.4307

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks
journal, December 1977

Wandzura, S.; Wilczek, F.
Physics Letters B, Vol. 72, Issue 2
https://doi.org/10.1016/0370-2693(77)90700-6

Generalized TMDs and the exclusive double Drell–Yan process
journal, August 2017

Bhattacharya, Shohini; Metz, Andreas; Zhou, Jian
Physics Letters B, Vol. 771
https://doi.org/10.1016/j.physletb.2017.05.081

Spin–orbit correlations in the nucleon
journal, July 2014

Lorcé, Cédric
Physics Letters B, Vol. 735
https://doi.org/10.1016/j.physletb.2014.06.068

Gauge-Invariant Decomposition of Nucleon Spin
journal, January 1997

Ji, Xiangdong
Physical Review Letters, Vol. 78, Issue 4
https://doi.org/10.1103/PhysRevLett.78.610

Quark Wigner distributions and orbital angular momentum
journal, July 2011

Lorcé, C.; Pasquini, B.
Physical Review D, Vol. 84, Issue 1
https://doi.org/10.1103/PhysRevD.84.014015

The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014

Leader, Elliot; Lorcé, Cédric
Physics Reports, Vol. 541, Issue 3
https://doi.org/10.1016/j.physrep.2014.02.010

Quantum Electrodynamics in the Infinite-Momentum Frame
journal, May 1970

Kogut, John B.; Soper, Davison E.
Physical Review D, Vol. 1, Issue 10
https://doi.org/10.1103/PhysRevD.1.2901

Proper definition and evolution of generalized transverse momentum dependent distributions
journal, August 2016

Echevarria, Miguel G.; Idilbi, Ahmad; Kanazawa, Koichi
Physics Letters B, Vol. 759
https://doi.org/10.1016/j.physletb.2016.05.086

Quark orbital angular momentum from Wigner distributions and light-cone wave functions
journal, June 2012

Lorcé, Cédric; Pasquini, Barbara; Xiong, Xiaonu
Physical Review D, Vol. 85, Issue 11
https://doi.org/10.1103/PhysRevD.85.114006

What can break the Wandzura-Wilczek relation?
journal, November 2009

Accardi, Alberto; Bacchetta, Alessandro; Melnitchouk, W.
Journal of High Energy Physics, Vol. 2009, Issue 11
https://doi.org/10.1088/1126-6708/2009/11/093

Parton orbital angular momentum and final state interactions
journal, July 2013

Burkardt, Matthias
Physical Review D, Vol. 88, Issue 1
https://doi.org/10.1103/PhysRevD.88.014014

The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990

Jaffe, R. L.; Manohar, Aneesh
Nuclear Physics B, Vol. 337, Issue 3
https://doi.org/10.1016/0550-3213(90)90506-9

Parton Physics on a Euclidean Lattice
journal, June 2013

Ji, Xiangdong
Physical Review Letters, Vol. 110, Issue 26
https://doi.org/10.1103/PhysRevLett.110.262002

Easy as π ^o : on the interpretation of recent electroproduction results
journal, October 2012

Goldstein, Gary R.; Hernandez, J. Osvaldo Gonzalez; Liuti, Simonetta
Journal of Physics G: Nuclear and Particle Physics, Vol. 39, Issue 11
https://doi.org/10.1088/0954-3899/39/11/115001

Parton transverse momentum and orbital angular momentum distributions
journal, August 2016

Rajan, Abha; Courtoy, Aurore; Engelhardt, Michael
Physical Review D, Vol. 94, Issue 3
https://doi.org/10.1103/PhysRevD.94.034041

Quark transverse spin–orbit correlations
journal, November 2017

Bhoonah, Amit; Lorcé, Cédric
Physics Letters B, Vol. 774
https://doi.org/10.1016/j.physletb.2017.10.003

Semi-inclusive deep inelastic scattering at small transverse momentum
journal, February 2007

Bacchetta, Alessandro; Diehl, Markus; Goeke, Klaus
Journal of High Energy Physics, Vol. 2007, Issue 02
https://doi.org/10.1088/1126-6708/2007/02/093

Generalized parton distributions with helicity flip
journal, March 2001

Diehl, M.
The European Physical Journal C, Vol. 19, Issue 3
https://doi.org/10.1007/s100520100635

Notes on the orbital angular momentum of quarks in the nucleon
journal, February 2012

Hatta, Yoshitaka
Physics Letters B, Vol. 708, Issue 1-2
https://doi.org/10.1016/j.physletb.2012.01.024

Wilson lines and orbital angular momentum
journal, February 2013

Lorcé, Cédric
Physics Letters B, Vol. 719, Issue 1-3
https://doi.org/10.1016/j.physletb.2013.01.007

Single-spin production asymmetries from the hard scattering of pointlike constituents
journal, January 1990

Sivers, Dennis
Physical Review D, Vol. 41, Issue 1
https://doi.org/10.1103/PhysRevD.41.83

Unraveling hadron structure with generalized parton distributions
journal, October 2005

Belitsky, A. V.; Radyushkin, A. V.
Physics Reports, Vol. 418, Issue 1-6
https://doi.org/10.1016/j.physrep.2005.06.002

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, January 1997

Mulders, P. J.; Tangerman, R. D.
Nuclear Physics B, Vol. 484, Issue 1-2
https://doi.org/10.1016/s0550-3213(96)00648-7

Gauge-invariant decomposition of nucleon spin
journal, June 2010

Wakamatsu, M.
Physical Review D, Vol. 81, Issue 11
https://doi.org/10.1103/physrevd.81.114010

Deeply virtual Compton scattering
journal, November 2015

Marukyan, Hrachya
International Journal of Modern Physics A, Vol. 30, Issue 32
https://doi.org/10.1142/s0217751x15300574

Works referencing / citing this record:

One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
journal, April 2019

Constantinou, Martha; Panagopoulos, Haralambos; Spanoudes, Gregoris
Physical Review D, Vol. 99, Issue 7
https://doi.org/10.1103/physrevd.99.074508

Similar records in OSTI.GOV collections:

Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: The role of the three-gluon correlator

Journal Article Dai, Ling-Yun ; Kang, Zhong-Bo ; Prokudin, Alexei ; ... - Physical Review. D, Particles, Fields, Gravitation and Cosmology

Here, we study the Sivers asymmetry in semi-inclusive hadron production in deep inelastic scattering. We concentrate on the contribution from the photon-gluon fusion channel at O(α _em ²α _s), where three-gluon correlation functions play a major role within the twist-3 collinear factorization formalism. We establish the correspondence between such a formalism with three-gluon correlation functions and the usual transverse momentum-dependent (TMD) factorization formalism at moderate hadron transverse momenta. We derive the coefficient functions used in the usual TMD evolution formalism related to the quark Sivers function expansion in terms of the three-gluon correlation functions. We further perform the next-to-leading ordermore »« less
Cited by 5
https://doi.org/10.1103/PhysRevD.92.114024

Full Text Available
Connections between collinear and transverse-momentum-dependent polarized observables within the Collins–Soper–Sterman formalism

Journal Article Gamberg, Leonard ; Metz, Andreas ; Pitonyak, Daniel ; ... - Physics Letters B

Here, we extend the improved Collins–Soper–Sterman (iCSS) W+Y construction recently presented in to the case of polarized observables, where we focus in particular on the Sivers effect in semi-inclusive deep-inelastic scattering. We further show how one recovers the expected leading-order collinear twist-3 result from a (weighted) q _T-integral of the differential cross section. We are also able to demonstrate the validity of the well-known relation between the (TMD) Sivers function and the (collinear twist-3) Qiu–Sterman function within the iCSS framework. This relation allows for their interpretation as functions yielding the average transverse momentum of unpolarized quarks in a transversely polarizedmore »« less
Cited by 3
https://doi.org/10.1016/j.physletb.2018.03.024
The spin structure of the nucleon

Journal Article Deur, Alexandre ; Brodsky, Stanley J. ; de Téramond, Guy F. - Reports on Progress in Physics

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. Inmore »« less
Cited by 9
https://doi.org/10.1088/1361-6633/ab0b8f

Full Text Available
QCD evolution of the orbital angular momentum of quarks and gluons: Genuine twist-three part

Journal Article Hatta, Yoshitaka ; Yao, Xiaojun - Physics Letters B

We present the numerical solution of the one-loop QCD evolution equation for the genuine twist- three part of the orbital angular momentum (OAM) distributions of quarks and gluons inside a longitudinally polarized nucleon. This is based on the observation that the evolution is identical to that of the Efremov-Teryaev-Qiu-Sterman function for transverse single spin asymmetry. Together with the known evolution of the Wandzura-Wilczek part, the one-loop evolution of OAM distribu- tions is now practically under control. We also study, for the rst time, the scale dependence of the potential angular momentum dened as the dierence between the Ji and Jae-Manoharmore » denitions of OAM.« less
https://doi.org/10.1016/j.physletb.2019.134941
Letter of Intent for a Drell-Yan Experiment with a Polarized Proton Target

Technical Report Geesaman, D. ; Reimer, P. ; Brown, C. ; ...

It is well known that the proton is a spin-1/2 particle, but how the constituents (quarks and gluons) assemble to this quantized spin is still a mystery. There is a worldwide effort to map out the individual contributions to the proton spin. It is established that the quark spins contribute around 30%, while the gluon intrinsic angular momentum is still under active investigation at the Relativistic Heavy Ion Collider. Fully resolving the proton spin puzzle requires information on the orbital angular momentum (OAM) of both quarks and gluons. Recent studies have shown that the so-called transverse momentum-dependent parton distribution functionsmore »« less
https://doi.org/10.2172/1296770

Full Text Available

Similar Records

Title: Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum

Abstract

Citation Formats

GPD phenomenology and DVCS fitting: Entering the high-precision era journal, June 2016

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, February 1996

Color, Spin, and Flavor-Dependent Forces in Quantum Chromodynamics conference, November 2011

Deeply virtual Compton scattering amplitude in the parton model journal, October 2000

Measurements of d 2 n and A 1 n : Probing the neutron spin structure journal, September 2016

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables journal, March 2016

Wigner, Husimi, and generalized transverse momentum dependent distributions in the color glass condensate journal, November 2016

Lorentz invariance relations among parton distributions revisited journal, August 2003

Power corrections at short distances journal, January 1980

Sivers and Boer-Mulders observables from lattice QCD journal, May 2012

Proton Spin Structure from Measurable Parton Distributions journal, October 2012

Deeply virtual Compton scattering journal, June 1997

Genuine twist-3 contributions to the generalized parton distributionsfrom instantons journal, September 2004

Lattice QCD study of the Boer-Mulders effect in a pion journal, March 2016

Quark orbital dynamics in the proton from lattice QCD: From Ji to Jaffe-Manohar orbital angular momentum journal, May 2017

Generalized parton correlation functions for a spin-1/2 hadron journal, August 2009

Twist analysis of the nucleon spin in QCD journal, October 2012

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects journal, November 2017

Generalized parton distributions journal, December 2003

Two-hadron semi-inclusive production including subleading twist contributions journal, April 2004

Exact sum rule for transversely polarized DIS journal, April 1997

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks journal, December 1977

Generalized TMDs and the exclusive double Drell–Yan process journal, August 2017

Spin–orbit correlations in the nucleon journal, July 2014

Gauge-Invariant Decomposition of Nucleon Spin journal, January 1997

Quark Wigner distributions and orbital angular momentum journal, July 2011

The angular momentum controversy: What’s it all about and does it matter? journal, August 2014

Quantum Electrodynamics in the Infinite-Momentum Frame journal, May 1970

Proper definition and evolution of generalized transverse momentum dependent distributions journal, August 2016

Quark orbital angular momentum from Wigner distributions and light-cone wave functions journal, June 2012

What can break the Wandzura-Wilczek relation? journal, November 2009

Parton orbital angular momentum and final state interactions journal, July 2013

The g1 problem: Deep inelastic electron scattering and the spin of the proton journal, June 1990

Parton Physics on a Euclidean Lattice journal, June 2013

Easy as π o : on the interpretation of recent electroproduction results journal, October 2012

Parton transverse momentum and orbital angular momentum distributions journal, August 2016

Quark transverse spin–orbit correlations journal, November 2017

Semi-inclusive deep inelastic scattering at small transverse momentum journal, February 2007

Generalized parton distributions with helicity flip journal, March 2001

Notes on the orbital angular momentum of quarks in the nucleon journal, February 2012

Wilson lines and orbital angular momentum journal, February 2013

Single-spin production asymmetries from the hard scattering of pointlike constituents journal, January 1990

Unraveling hadron structure with generalized parton distributions journal, October 2005

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction journal, January 1997

Gauge-invariant decomposition of nucleon spin journal, June 2010

Deeply virtual Compton scattering journal, November 2015

One-loop renormalization of staple-shaped operators in continuum and lattice regularizations journal, April 2019

GPD phenomenology and DVCS fitting: Entering the high-precision era
journal, June 2016

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996

Color, Spin, and Flavor-Dependent Forces in Quantum Chromodynamics
conference, November 2011

Deeply virtual Compton scattering amplitude in the parton model
journal, October 2000

Measurements of $d_{2}^{n}$ and $A_{1}^{n}$ : Probing the neutron spin structure
journal, September 2016

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables
journal, March 2016

Wigner, Husimi, and generalized transverse momentum dependent distributions in the color glass condensate
journal, November 2016

Lorentz invariance relations among parton distributions revisited
journal, August 2003

Power corrections at short distances
journal, January 1980

Sivers and Boer-Mulders observables from lattice QCD
journal, May 2012

Proton Spin Structure from Measurable Parton Distributions
journal, October 2012

Deeply virtual Compton scattering
journal, June 1997

Genuine twist-3 contributions to the generalized parton distributionsfrom instantons
journal, September 2004

Lattice QCD study of the Boer-Mulders effect in a pion
journal, March 2016

Quark orbital dynamics in the proton from lattice QCD: From Ji to Jaffe-Manohar orbital angular momentum
journal, May 2017

Generalized parton correlation functions for a spin-1/2 hadron
journal, August 2009

Twist analysis of the nucleon spin in QCD
journal, October 2012

Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects
journal, November 2017

Generalized parton distributions
journal, December 2003

Two-hadron semi-inclusive production including subleading twist contributions
journal, April 2004

Exact sum rule for transversely polarized DIS
journal, April 1997

Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks
journal, December 1977

Generalized TMDs and the exclusive double Drell–Yan process
journal, August 2017

Spin–orbit correlations in the nucleon
journal, July 2014

Gauge-Invariant Decomposition of Nucleon Spin
journal, January 1997

Quark Wigner distributions and orbital angular momentum
journal, July 2011

The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014

Quantum Electrodynamics in the Infinite-Momentum Frame
journal, May 1970

Proper definition and evolution of generalized transverse momentum dependent distributions
journal, August 2016

Quark orbital angular momentum from Wigner distributions and light-cone wave functions
journal, June 2012

What can break the Wandzura-Wilczek relation?
journal, November 2009

Parton orbital angular momentum and final state interactions
journal, July 2013

The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990

Parton Physics on a Euclidean Lattice
journal, June 2013

Easy as π ^o : on the interpretation of recent electroproduction results
journal, October 2012

Parton transverse momentum and orbital angular momentum distributions
journal, August 2016

Quark transverse spin–orbit correlations
journal, November 2017

Semi-inclusive deep inelastic scattering at small transverse momentum
journal, February 2007

Generalized parton distributions with helicity flip
journal, March 2001

Notes on the orbital angular momentum of quarks in the nucleon
journal, February 2012

Wilson lines and orbital angular momentum
journal, February 2013

Single-spin production asymmetries from the hard scattering of pointlike constituents
journal, January 1990

Unraveling hadron structure with generalized parton distributions
journal, October 2005

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, January 1997

Gauge-invariant decomposition of nucleon spin
journal, June 2010

Deeply virtual Compton scattering
journal, November 2015

One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
journal, April 2019