Finite-volume effects due to spatially nonlocal operators

Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.; Monahan, Christopher J.

doi:10.1103/PhysRevD.98.014511

Title: Finite-volume effects due to spatially nonlocal operators

Abstract

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. In order to quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work we estimate these effects by considering a simple toy model in which the non-local operator is composed of two currents displaced in a spatial direction by a distance $$\xi$$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $$ e^{-m_\pi (L- \xi)} $$, where $$m$$ is the mass of the light state. For heavier external states the usual $$e^{- m_\pi L}$$ form is recovered, but with a polynomial prefactor of the form $$L^a/|L - \xi|^b$$ that can lead to enhanced volume effects. As a result, these observations {might be relevant} for a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta decay and Compton scattering matrix elements, and long-range weak matrix elements.

Authors:: Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.; Monahan, Christopher J.

Publication Date:: Thu Jul 26 00:00:00 EDT 2018

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1461723

Alternate Identifier(s):: OSTI ID: 1462022

Report Number(s):: JLAB-THY-18-2697; DOE/OR/23177-4429; arXiv:1805.01034; CERN-TH-2018-109; INT-PUB-18-019
Journal ID: ISSN 2470-0010; PRVDAQ; 014511

Grant/Contract Number:: AC05-06OR23177; SC0008791; FG02-00ER41132

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Briceño, Raúl A., Guerrero, Juan V., Hansen, Maxwell T., and Monahan, Christopher J. Finite-volume effects due to spatially nonlocal operators.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.014511.

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                    Briceño, Raúl A., Guerrero, Juan V., Hansen, Maxwell T., & Monahan, Christopher J. Finite-volume effects due to spatially nonlocal operators.  United States.  https://doi.org/10.1103/PhysRevD.98.014511

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                    Briceño, Raúl A., Guerrero, Juan V., Hansen, Maxwell T., and Monahan, Christopher J. Thu .  
"Finite-volume effects due to spatially nonlocal operators".  United States.  https://doi.org/10.1103/PhysRevD.98.014511.

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@article{osti_1461723,

  title        = {Finite-volume effects due to spatially nonlocal operators},

  author       = {Briceño, Raúl A. and Guerrero, Juan V. and Hansen, Maxwell T. and Monahan, Christopher J.},

  abstractNote = {Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. In order to quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work we estimate these effects by considering a simple toy model in which the non-local operator is composed of two currents displaced in a spatial direction by a distance $\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\pi (L- \xi)} $, where $m$ is the mass of the light state. For heavier external states the usual $e^{- m_\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^a/|L - \xi|^b$ that can lead to enhanced volume effects. As a result, these observations {might be relevant} for a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta decay and Compton scattering matrix elements, and long-range weak matrix elements.},

  doi          = {10.1103/PhysRevD.98.014511},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 98,

  place        = {United States},

  year         = {Thu Jul 26 00:00:00 EDT 2018},

  month        = {Thu Jul 26 00:00:00 EDT 2018}

}

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Works referenced in this record:

Physics opportunities with the 12 GeV upgrade at Jefferson Lab
journal, December 2012

Dudek, Jozef; Ent, Rolf; Essig, Rouven
The European Physical Journal A, Vol. 48, Issue 12
DOI: 10.1140/epja/i2012-12187-1

Exclusive processes in position space and the pion distribution amplitude
journal, May 2008

Braun, V. M.; Müller, D.
The European Physical Journal C, Vol. 55, Issue 3
DOI: 10.1140/epjc/s10052-008-0608-4

Generalized parton distributions for the pion in chiral perturbation theory
journal, August 2005

Diehl, M.; Manashov, A.; Schäfer, A.
Physics Letters B, Vol. 622, Issue 1-2
DOI: 10.1016/j.physletb.2005.06.079

Baryon axial charge in a finite volume
journal, October 2004

Beane, S. R.; Savage, M. J.
Physical Review D, Vol. 70, Issue 7
DOI: 10.1103/PhysRevD.70.074029

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

Lüscher, M.
Communications in Mathematical Physics, Vol. 104, Issue 2
DOI: 10.1007/BF01211589

The pion mass in finite volume
journal, March 2004

Colangelo, G.; Dürr, S.
The European Physical Journal C, Vol. 33, Issue 4
DOI: 10.1140/epjc/s2004-01593-y

Parton distributions and lattice QCD calculations: A community white paper
journal, May 2018

Lin, Huey-Wen; Nocera, Emanuele R.; Olness, Fred
Progress in Particle and Nuclear Physics, Vol. 100
DOI: 10.1016/j.ppnp.2018.01.007

Novel quark smearing for hadrons with high momenta in lattice QCD
journal, May 2016

Bali, Gunnar S.; Lang, Bernhard; Musch, Bernhard U.
Physical Review D, Vol. 93, Issue 9
DOI: 10.1103/PhysRevD.93.094515

Finite size effects onMπ in QCD from chiral perturbation theory
journal, May 2003

Colangelo, G.; Du¨rr, S.; Sommer, R.
Nuclear Physics B - Proceedings Supplements, Vol. 119
DOI: 10.1016/S0920-5632(03)80450-4

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations
journal, January 2018

Ma, Yan-Qing; Qiu, Jian-Wei
Physical Review Letters, Vol. 120, Issue 2
DOI: 10.1103/PhysRevLett.120.022003

The Resolving Power of Gross Earth Data
journal, October 1968

Backus, George; Gilbert, Freeman
Geophysical Journal International, Vol. 16, Issue 2
DOI: 10.1111/j.1365-246X.1968.tb00216.x

Exponential reduction of finite volume effects with twisted boundary conditions
journal, April 2017

Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L.
Physical Review D, Vol. 95, Issue 7
DOI: 10.1103/PhysRevD.95.074512

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

Lellouch, Laurent; Lüscher, Martin
Communications in Mathematical Physics, Vol. 219, Issue 1
DOI: 10.1007/s002200100410

Perturbative renormalization of quasi-parton distribution functions
journal, September 2017

Constantinou, Martha; Panagopoulos, Haralambos
Physical Review D, Vol. 96, Issue 5
DOI: 10.1103/PhysRevD.96.054506

Constructing Parton Convolution in Effective Field Theory
journal, September 2001

Chen, Jiunn-Wei; Ji, Xiangdong
Physical Review Letters, Vol. 87, Issue 15
DOI: 10.1103/PhysRevLett.87.152002

Progress in computing parton distribution functions from the quasi-PDF approach
journal, January 2018

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
EPJ Web of Conferences, Vol. 175
DOI: 10.1051/epjconf/201817506021

Two-loop sunset integrals at finite volume
journal, January 2014

Bijnens, Johan; Boström, Emil; Lähde, Timo A.
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)019

Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders
journal, July 1961

Byers, N.; Yang, C. N.
Physical Review Letters, Vol. 7, Issue 2
DOI: 10.1103/PhysRevLett.7.46

Parton Physics on a Euclidean Lattice
journal, June 2013

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

Nucleon Structure Functions from Operator Product Expansion on the Lattice
journal, June 2017

Chambers, A. J.; Horsley, R.; Nakamura, Y.
Physical Review Letters, Vol. 118, Issue 24
DOI: 10.1103/PhysRevLett.118.242001

Model independent determination of the light-cone wave functions for exclusive processes
journal, November 1998

Aglietti, U.; Ciuchini, M.; Corbò, G.
Physics Letters B, Vol. 441, Issue 1-4
DOI: 10.1016/S0370-2693(98)01138-1

Renormalizability of quasiparton distribution functions
journal, November 2017

Ishikawa, Tomomi; Ma, Yan-Qing; Qiu, Jian-Wei
Physical Review D, Vol. 96, Issue 9
DOI: 10.1103/PhysRevD.96.094019

Effective chiral lagrangians for nucleon-pion interactions and nuclear forces
journal, September 1991

Weinberg, Steven
Nuclear Physics B, Vol. 363, Issue 1
DOI: 10.1016/0550-3213(91)90231-L

Two-baryon systems with twisted boundary conditions
journal, April 2014

Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
Physical Review D, Vol. 89, Issue 7
DOI: 10.1103/PhysRevD.89.074509

Lattice calculation of parton distributions
journal, July 2015

Alexandrou, Constantia; Cichy, Krzysztof; Drach, Vincent
Physical Review D, Vol. 92, Issue 1
DOI: 10.1103/PhysRevD.92.014502

An asymptotic formula for the pion decay constant in a large volume
journal, June 2004

Colangelo, Gilberto; Haefeli, Christoph
Physics Letters B, Vol. 590, Issue 3-4
DOI: 10.1016/j.physletb.2004.03.080

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004

Bedaque, Paulo F.
Physics Letters B, Vol. 593, Issue 1-4
DOI: 10.1016/j.physletb.2004.04.045

Nuclear forces from chiral lagrangians
journal, November 1990

Weinberg, Steven
Physics Letters B, Vol. 251, Issue 2
DOI: 10.1016/0370-2693(90)90938-3

Pion distribution amplitude from Euclidean correlation functions
journal, March 2018

Bali, Gunnar S.; Braun, Vladimir M.; Gläßle, Benjamin
The European Physical Journal C, Vol. 78, Issue 3
DOI: 10.1140/epjc/s10052-018-5700-9

On the chiral expansion for parton distributions at small <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:mi>x</mml:mi><mml:mo>∼</mml:mo><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math>
journal, June 2008

Kivel, N.; Polyakov, M. V.
Physics Letters B, Vol. 664, Issue 1-2
DOI: 10.1016/j.physletb.2008.04.048

Nucleon masses and magnetic moments in a finite volume
journal, August 2004

Beane, Silas R.
Physical Review D, Vol. 70, Issue 3
DOI: 10.1103/PhysRevD.70.034507

Nonperturbative evolution of parton quasi-distributions
journal, April 2017

Radyushkin, A. V.
Physics Letters B, Vol. 767
DOI: 10.1016/j.physletb.2017.02.019

Effects of finite volume on the $K_{L} - K_{S}$ mass difference
journal, June 2015

Christ, N. H.; Feng, X.; Martinelli, G.
Physical Review D, Vol. 91, Issue 11
DOI: 10.1103/PhysRevD.91.114510

Erratum: Constructing Parton Convolution in Effective Field Theory [Phys. Rev. Lett. 87, 152002 (2001)]
journal, May 2002

Chen, Jiunn-Wei; Ji, Xiangdong
Physical Review Letters, Vol. 88, Issue 24
DOI: 10.1103/PhysRevLett.88.249901

Chiral perturbation theory for hadrons containing a heavy quark
journal, April 1992

Wise, Mark B.
Physical Review D, Vol. 45, Issue 7
DOI: 10.1103/PhysRevD.45.R2188

Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006

Detmold, William; Lin, C. -J. David
Physical Review D, Vol. 73, Issue 1
DOI: 10.1103/PhysRevD.73.014501

Lattice QCD exploration of parton pseudo-distribution functions
journal, November 2017

Orginos, Kostas; Radyushkin, Anatoly; Karpie, Joseph
Physical Review D, Vol. 96, Issue 9
DOI: 10.1103/PhysRevD.96.094503

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements
journal, July 2017

Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.
Physical Review D, Vol. 96, Issue 1
DOI: 10.1103/PhysRevD.96.014502

Parton distribution function with nonperturbative renormalization from lattice QCD
journal, January 2018

Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang
Physical Review D, Vol. 97, Issue 1
DOI: 10.1103/PhysRevD.97.014505

A complete non-perturbative renormalization prescription for quasi-PDFs
journal, October 2017

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Nuclear Physics B, Vol. 923
DOI: 10.1016/j.nuclphysb.2017.08.012

Uniqueness in the Inversion of Inaccurate Gross Earth Data
journal, March 1970

Backus, G.; Gilbert, F.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 266, Issue 1173
DOI: 10.1098/rsta.1970.0005

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions
journal, August 2017

Radyushkin, A. V.
Physical Review D, Vol. 96, Issue 3
DOI: 10.1103/PhysRevD.96.034025

Quasi parton distributions and the gradient flow
journal, March 2017

Monahan, Christopher; Orginos, Kostas
Journal of High Energy Physics, Vol. 2017, Issue 3
DOI: 10.1007/JHEP03(2017)116

Applying twisted boundary conditions for few-body nuclear systems
journal, May 2016

Körber, Christopher; Luu, Thomas
Physical Review C, Vol. 93, Issue 5
DOI: 10.1103/PhysRevC.93.054002

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016

Accardi, A.; Albacete, J. L.; Anselmino, M.
The European Physical Journal A, Vol. 52, Issue 9
DOI: 10.1140/epja/i2016-16268-9

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017

Hansen, Maxwell T.; Meyer, Harvey B.; Robaina, Daniel
Physical Review D, Vol. 96, Issue 9
DOI: 10.1103/PhysRevD.96.094513

Parton distribution functions from reduced Ioffe-time distributions
journal, April 2018

Zhang, Jian-Hui; Chen, Jiunn-Wei; Monahan, Christopher
Physical Review D, Vol. 97, Issue 7
DOI: 10.1103/PhysRevD.97.074508

Flavor structure of the nucleon sea from lattice QCD
journal, March 2015

Lin, Huey-Wen; Chen, Jiunn-Wei; Cohen, Saul D.
Physical Review D, Vol. 91, Issue 5
DOI: 10.1103/PhysRevD.91.054510

Nucleon helicity and transversity parton distributions from lattice QCD
journal, October 2016

Chen, Jiunn-Wei; Cohen, Saul D.; Ji, Xiangdong
Nuclear Physics B, Vol. 911
DOI: 10.1016/j.nuclphysb.2016.07.033

Renormalization in Large Momentum Effective Theory of Parton Physics
journal, March 2018

Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong
Physical Review Letters, Vol. 120, Issue 11
DOI: 10.1103/PhysRevLett.120.112001

Target mass effects in parton quasi-distributions
journal, July 2017

Radyushkin, A. V.
Physics Letters B, Vol. 770
DOI: 10.1016/j.physletb.2017.05.024

Preliminaries on a lattice analysis of the pion light-cone wave function: A partonic signal?
journal, September 2001

Abada, A.; Boucaud, Ph.; Herdoiza, G.
Physical Review D, Vol. 64, Issue 7
DOI: 10.1103/PhysRevD.64.074511

Updated lattice results for parton distributions
journal, July 2017

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Physical Review D, Vol. 96, Issue 1
DOI: 10.1103/PhysRevD.96.014513

Updated lattice results for parton distributions
text, January 2017

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2017-09401

Works referencing / citing this record:

Light-Cone Parton Distribution Functions from Lattice QCD
text, January 2018

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-03714

Hadrons and nuclei
journal, November 2019

Detmold, William; Edwards, Robert G.; Dudek, Jozef J.
The European Physical Journal A, Vol. 55, Issue 11
DOI: 10.1140/epja/i2019-12902-4

Lattice QCD and neutrino-nucleus scattering
journal, November 2019

Kronfeld, Andreas S.; Richards, David G.; Detmold, William
The European Physical Journal A, Vol. 55, Issue 11
DOI: 10.1140/epja/i2019-12916-x

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019

Cichy, Krzysztof; Constantinou, Martha
Advances in High Energy Physics, Vol. 2019
DOI: 10.1155/2019/3036904

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
text, January 2019

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-02720

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Title: Finite-volume effects due to spatially nonlocal operators

Abstract

Citation Formats

Physics opportunities with the 12 GeV upgrade at Jefferson Lab journal, December 2012

Exclusive processes in position space and the pion distribution amplitude journal, May 2008

Generalized parton distributions for the pion in chiral perturbation theory journal, August 2005

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Parton distributions and lattice QCD calculations: A community white paper journal, May 2018

Novel quark smearing for hadrons with high momenta in lattice QCD journal, May 2016

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Exponential reduction of finite volume effects with twisted boundary conditions journal, April 2017

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions journal, May 2001

Perturbative renormalization of quasi-parton distribution functions journal, September 2017

Constructing Parton Convolution in Effective Field Theory journal, September 2001

Progress in computing parton distribution functions from the quasi-PDF approach journal, January 2018

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Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders journal, July 1961

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Nucleon Structure Functions from Operator Product Expansion on the Lattice journal, June 2017

Model independent determination of the light-cone wave functions for exclusive processes journal, November 1998

Renormalizability of quasiparton distribution functions journal, November 2017

Effective chiral lagrangians for nucleon-pion interactions and nuclear forces journal, September 1991

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Lattice calculation of parton distributions journal, July 2015

An asymptotic formula for the pion decay constant in a large volume journal, June 2004

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice journal, July 2004

Nuclear forces from chiral lagrangians journal, November 1990

Pion distribution amplitude from Euclidean correlation functions journal, March 2018

Nucleon masses and magnetic moments in a finite volume journal, August 2004

Nonperturbative evolution of parton quasi-distributions journal, April 2017

Effects of finite volume on the K L − K S mass difference journal, June 2015

Erratum: Constructing Parton Convolution in Effective Field Theory [Phys. Rev. Lett. 87, 152002 (2001)] journal, May 2002

Chiral perturbation theory for hadrons containing a heavy quark journal, April 1992

Deep-inelastic scattering and the operator product expansion in lattice QCD journal, January 2006

Lattice QCD exploration of parton pseudo-distribution functions journal, November 2017

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements journal, July 2017

Parton distribution function with nonperturbative renormalization from lattice QCD journal, January 2018

A complete non-perturbative renormalization prescription for quasi-PDFs journal, October 2017

Uniqueness in the Inversion of Inaccurate Gross Earth Data journal, March 1970

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions journal, August 2017

Quasi parton distributions and the gradient flow journal, March 2017

Applying twisted boundary conditions for few-body nuclear systems journal, May 2016

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all journal, September 2016

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD journal, November 2017

Parton distribution functions from reduced Ioffe-time distributions journal, April 2018

Flavor structure of the nucleon sea from lattice QCD journal, March 2015

Nucleon helicity and transversity parton distributions from lattice QCD journal, October 2016

Renormalization in Large Momentum Effective Theory of Parton Physics journal, March 2018

Target mass effects in parton quasi-distributions journal, July 2017

Preliminaries on a lattice analysis of the pion light-cone wave function: A partonic signal? journal, September 2001

Updated lattice results for parton distributions journal, July 2017

Updated lattice results for parton distributions text, January 2017

Light-Cone Parton Distribution Functions from Lattice QCD text, January 2018

Hadrons and nuclei journal, November 2019

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Physics opportunities with the 12 GeV upgrade at Jefferson Lab
journal, December 2012

Exclusive processes in position space and the pion distribution amplitude
journal, May 2008

Generalized parton distributions for the pion in chiral perturbation theory
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Baryon axial charge in a finite volume
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The pion mass in finite volume
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Parton distributions and lattice QCD calculations: A community white paper
journal, May 2018

Novel quark smearing for hadrons with high momenta in lattice QCD
journal, May 2016

Finite size effects onMπ in QCD from chiral perturbation theory
journal, May 2003

Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations
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The Resolving Power of Gross Earth Data
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Exponential reduction of finite volume effects with twisted boundary conditions
journal, April 2017

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

Perturbative renormalization of quasi-parton distribution functions
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Constructing Parton Convolution in Effective Field Theory
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Progress in computing parton distribution functions from the quasi-PDF approach
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Parton Physics on a Euclidean Lattice
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Nucleon Structure Functions from Operator Product Expansion on the Lattice
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Model independent determination of the light-cone wave functions for exclusive processes
journal, November 1998

Renormalizability of quasiparton distribution functions
journal, November 2017

Effective chiral lagrangians for nucleon-pion interactions and nuclear forces
journal, September 1991

Two-baryon systems with twisted boundary conditions
journal, April 2014

Lattice calculation of parton distributions
journal, July 2015

An asymptotic formula for the pion decay constant in a large volume
journal, June 2004

Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004

Nuclear forces from chiral lagrangians
journal, November 1990

Pion distribution amplitude from Euclidean correlation functions
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Nucleon masses and magnetic moments in a finite volume
journal, August 2004

Nonperturbative evolution of parton quasi-distributions
journal, April 2017

Effects of finite volume on the $K_{L} - K_{S}$ mass difference
journal, June 2015

Erratum: Constructing Parton Convolution in Effective Field Theory [Phys. Rev. Lett. 87, 152002 (2001)]
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Chiral perturbation theory for hadrons containing a heavy quark
journal, April 1992

Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006

Lattice QCD exploration of parton pseudo-distribution functions
journal, November 2017

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements
journal, July 2017

Parton distribution function with nonperturbative renormalization from lattice QCD
journal, January 2018

A complete non-perturbative renormalization prescription for quasi-PDFs
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Uniqueness in the Inversion of Inaccurate Gross Earth Data
journal, March 1970

Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions
journal, August 2017

Quasi parton distributions and the gradient flow
journal, March 2017

Applying twisted boundary conditions for few-body nuclear systems
journal, May 2016

Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017

Parton distribution functions from reduced Ioffe-time distributions
journal, April 2018

Flavor structure of the nucleon sea from lattice QCD
journal, March 2015

Nucleon helicity and transversity parton distributions from lattice QCD
journal, October 2016

Renormalization in Large Momentum Effective Theory of Parton Physics
journal, March 2018

Target mass effects in parton quasi-distributions
journal, July 2017

Preliminaries on a lattice analysis of the pion light-cone wave function: A partonic signal?
journal, September 2001

Updated lattice results for parton distributions
journal, July 2017

Updated lattice results for parton distributions
text, January 2017

Light-Cone Parton Distribution Functions from Lattice QCD
text, January 2018

Hadrons and nuclei
journal, November 2019

Lattice QCD and neutrino-nucleus scattering
journal, November 2019

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
text, January 2019