First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function

Zhang, Jian-Hui; Chen, Jiunn-Wei; Jin, Luchang; Lin, Huey-Wen; Schäfer, Andreas; Zhao, Yong

doi:10.1103/PhysRevD.100.034505

Title: First direct lattice-QCD calculation of the $x$ -dependence of the pion parton distribution function

Abstract

We present the first direct lattice-QCD calculation of the Bjorken-x dependence of the valence quark distribution of the pion. Using large-momentum effective theory (LaMET), we calculate the boosted pion state with long Wilson link operators. After implementing the one-loop matching and meson mass corrections, our result at m π ≈ 310 MeV is in agreement with those extracted from experimental data as well as from the Dyson-Schwinger equation in the small-x region, but there is a sizeable discrepancy in the large-x region. This discrepancy provides a nice opportunity to systematically study and disentangle the artifacts in the LaMET approach, which will eventually help to discern various existing analyses in the literature.

Authors:

Zhang, Jian-Hui; Chen, Jiunn-Wei; Jin, Luchang; Lin, Huey-Wen; Schäfer, Andreas; Zhao, Yong; Lattice Parton Physics Project ^[1]

(LP³)

Publication Date:: 2019-08-08

Research Org.:: Univ. of Connecticut, Storrs, CT (United States)

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

Contributing Org.:: Lattice Parton Physics Project (LP³)

OSTI Identifier:: 1550587

Alternate Identifier(s):: OSTI ID: 1596006

Grant/Contract Number:: AC02-05CH11231; SC0011090; EC0012704; SC0010339

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; 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

Citation Formats


                    Zhang, Jian-Hui, Chen, Jiunn-Wei, Jin, Luchang, Lin, Huey-Wen, Schäfer, Andreas, Zhao, Yong, and Lattice Parton Physics Project. First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.034505.

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                    Zhang, Jian-Hui, Chen, Jiunn-Wei, Jin, Luchang, Lin, Huey-Wen, Schäfer, Andreas, Zhao, Yong, & Lattice Parton Physics Project. First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function.  United States.  https://doi.org/10.1103/PhysRevD.100.034505

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                    Zhang, Jian-Hui, Chen, Jiunn-Wei, Jin, Luchang, Lin, Huey-Wen, Schäfer, Andreas, Zhao, Yong, and Lattice Parton Physics Project. Thu .  
"First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function".  United States.  https://doi.org/10.1103/PhysRevD.100.034505.

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@article{osti_1550587,

  title        = {First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function},

  author       = {Zhang, Jian-Hui and Chen, Jiunn-Wei and Jin, Luchang and Lin, Huey-Wen and Schäfer, Andreas and Zhao, Yong and Lattice Parton Physics Project},

  abstractNote = {We present the first direct lattice-QCD calculation of the Bjorken-x dependence of the valence quark distribution of the pion. Using large-momentum effective theory (LaMET), we calculate the boosted pion state with long Wilson link operators. After implementing the one-loop matching and meson mass corrections, our result at m π ≈ 310 MeV is in agreement with those extracted from experimental data as well as from the Dyson-Schwinger equation in the small-x region, but there is a sizeable discrepancy in the large-x region. This discrepancy provides a nice opportunity to systematically study and disentangle the artifacts in the LaMET approach, which will eventually help to discern various existing analyses in the literature.},

  doi          = {10.1103/PhysRevD.100.034505},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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We present a state-of-the-art calculation of the isovector quark helicity Bjorken-x distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta P_z ϵ {2.2; 2.6; 3.0} GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET).We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data; in particular, Δmore » $$\bar{u}$$(x) > Δ$$\bar{d}$$(x).« less
Cited by 15
https://doi.org/10.1103/PhysRevLett.121.242003

Full Text Available
Machine-learning prediction for quasiparton distribution function matrix elements

Journal Article Zhang, Rui ; Fan, Zhouyou ; Li, Ruizi ; ... - Physical Review D

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-x dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken x) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small- x reliably. This means that very fine lattice spacing to minimize lattice artifacts at ordermore »« less
Cited by 2
https://doi.org/10.1103/PhysRevD.101.034516
Kaon distribution amplitude from lattice QCD and the flavor SU(3) symmetry

Journal Article Zhang, Rui ; Chen, Jiunn-Wei ; Jin, Luchang ; ... - Nuclear Physics. B

We present the first lattice-QCD calculation of the kaon distribution amplitude using the large-momentum effective theory (LaMET) approach. The momentum-smearing technique has been implemented to improve signals at large meson momenta. We subtract the power divergence due to Wilson line to high precision using multiple lattice spacings. The kaon structure clearly shows an asymmetry of the distribution amplitude around x = 1/2, a clear sign of its skewness. Our result also prefers a broader distribution than the asymptotic form. We also study the leading SU(3) flavor symmetry breaking relations for the pion, kaon and eta meson distribution amplitudes, and themore »« less
Cited by 15
https://doi.org/10.1016/j.nuclphysb.2018.12.020

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Title: First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function

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Citation Formats

Dyson–Schwinger Equations: A Tool for Hadron Physics journal, June 2003

Improved parton distribution functions at the physical pion mass journal, September 2018

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

Phenomenological Model for the Electromagnetic Structure of the Proton journal, May 1970

New parton distribution functions from a global analysis of quantum chromodynamics journal, February 2016

Quantifying finite-momentum effects in the quark quasidistribution functions of mesons journal, March 2018

Constraints on large- x parton distributions from new weak boson production and deep-inelastic scattering data journal, June 2016

Isovector and isoscalar tensor charges of the nucleon from lattice QCD journal, November 2015

Factorization theorem relating Euclidean and light-cone parton distributions journal, September 2018

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

Factorization of large-x quark distributions in a hadron journal, March 2005

Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field journal, July 2018

Nondipolar Wilson links for quasiparton distribution functions journal, October 2016

Pion structure function in the Nambu and Jona-Lasinio model journal, July 1993

Nucleon charges and electromagnetic form factors from 2 + 1 + 1 -flavor lattice QCD journal, May 2014

On the power divergence in quasi gluon distribution function journal, May 2018

Flavor symmetry and the static potential with hypercubic blocking journal, July 2001

Kaon distribution amplitude from lattice QCD and the flavor SU(3) symmetry journal, February 2019

Smeared quasidistributions in perturbation theory journal, March 2018

Gluon quasidistribution function at one loop journal, February 2018

Lattice calculation of hadronic tensor of the nucleon journal, January 2018

Parton physics from large-momentum effective field theory journal, May 2014

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

Generalized relativistic meson wave function journal, April 1994

Quark-hadron duality in electron-pion scattering journal, June 2003

Angular distributions of muon pairs produced by 194 GeV/c negative pions journal, December 1986

Experimental study of muon pairs produced by 252-GeV pions on tungsten journal, January 1989

Renormalization of quasiparton distribution journal, August 2015

One-loop matching for transversity generalized parton distribution journal, September 2015

Transverse momentum dependent parton quasidistributions journal, June 2019

Axial-vector form factors of the nucleon from lattice QCD journal, December 2017

Parton distributions from high-precision collider data: NNPDF Collaboration journal, October 2017

Parton Physics on a Euclidean Lattice journal, June 2013

Extracting parton distribution functions from lattice QCD calculations journal, October 2018

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

One-loop matching for parton distributions: Nonsinglet case journal, July 2014

Quasi-parton distribution functions: A study in the diquark spectator model journal, April 2015

Renormalizability of quasiparton distribution functions journal, November 2017

Gluon helicity Δ G from a universality class of operators on a lattice journal, April 2014

QCD constraints on the shape of polarized quark and gluon distributions journal, May 1995

Highly improved staggered quarks on the lattice with applications to charm physics journal, March 2007

Light-Cone Parton Distribution Functions from Lattice QCD journal, September 2018

Pion distribution amplitude from lattice QCD journal, May 2017

Soft factor subtraction and transverse momentum dependent parton distributions on the lattice journal, April 2015

Experimental determination of the π meson structure functions by the Drell-Yan mechanism journal, December 1983

One-loop evolution of parton pseudo-distribution functions on the lattice journal, July 2018

Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion journal, December 2010

Neutron Electric Dipole Moment and Tensor Charges from Lattice QCD journal, November 2015

Solving the Bars-Green equation for moving mesons in two-dimensional QCD journal, November 2017

Origin of difference between u ¯ and d ¯ partons in the nucleon journal, March 1994

Lattice calculation of parton distributions journal, July 2015

Structure functions of pseudoscalar mesons in the SU(3) NJL model journal, March 1995

Gaussian-weighted parton quasi-distribution (Lattice Parton Physics Project (LP3)) journal, April 2019

Pion distribution amplitude from Euclidean correlation functions journal, March 2018

Lattice QCD ensembles with four flavors of highly improved staggered quarks journal, March 2013

Pion parton distribution function in the valence region journal, December 2005

Nonperturbative evolution of parton quasi-distributions journal, April 2017

Deep-inelastic structure function of the pion in the null-plane phenomenology journal, July 1994

Improved quasi parton distribution through Wilson line renormalization journal, February 2017

Angular distributions of muon pairs produced by negative pions on deuterium and tungsten journal, December 1988

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

Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model journal, December 2017

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

Lattice corrections to the quark quasidistribution at one loop journal, May 2017

Nucleon and pion distribution functions in the valence region journal, October 2010

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

Note on lattice regularization and equal-time correlators for parton distribution functions journal, July 2017

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

One-loop matching for generalized parton distributions journal, July 2015

Light-cone distribution amplitudes of vector meson in a large momentum effective theory journal, June 2018

Pion and Nucleon Structure Functions near x = 1 journal, November 1975

Pion and kaon valence-quark parton distribution functions journal, June 2011

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

Nonperturbative partonic quasidistributions of the pion from chiral quark models journal, October 2017

Matching the quasiparton distribution in a momentum subtraction scheme journal, March 2018

Valence-quark distribution functions in the kaon and pion journal, April 2016

Quasi parton distributions and the gradient flow journal, March 2017

Title: First direct lattice-QCD calculation of the $x$ -dependence of the pion parton distribution function

Dyson–Schwinger Equations: A Tool for Hadron Physics
journal, June 2003

Improved parton distribution functions at the physical pion mass
journal, September 2018

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

Phenomenological Model for the Electromagnetic Structure of the Proton
journal, May 1970

New parton distribution functions from a global analysis of quantum chromodynamics
journal, February 2016

Quantifying finite-momentum effects in the quark quasidistribution functions of mesons
journal, March 2018

Constraints on large- $x$ parton distributions from new weak boson production and deep-inelastic scattering data
journal, June 2016

Isovector and isoscalar tensor charges of the nucleon from lattice QCD
journal, November 2015

Factorization theorem relating Euclidean and light-cone parton distributions
journal, September 2018

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

Factorization of large-x quark distributions in a hadron
journal, March 2005

Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field
journal, July 2018

Nondipolar Wilson links for quasiparton distribution functions
journal, October 2016

Pion structure function in the Nambu and Jona-Lasinio model
journal, July 1993

Nucleon charges and electromagnetic form factors from $2 + 1 + 1$ -flavor lattice QCD
journal, May 2014

On the power divergence in quasi gluon distribution function
journal, May 2018

Flavor symmetry and the static potential with hypercubic blocking
journal, July 2001

Kaon distribution amplitude from lattice QCD and the flavor SU(3) symmetry
journal, February 2019

Smeared quasidistributions in perturbation theory
journal, March 2018

Gluon quasidistribution function at one loop
journal, February 2018

Lattice calculation of hadronic tensor of the nucleon
journal, January 2018

Parton physics from large-momentum effective field theory
journal, May 2014

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

Generalized relativistic meson wave function
journal, April 1994

Quark-hadron duality in electron-pion scattering
journal, June 2003

Angular distributions of muon pairs produced by 194 GeV/c negative pions
journal, December 1986

Experimental study of muon pairs produced by 252-GeV pions on tungsten
journal, January 1989

Renormalization of quasiparton distribution
journal, August 2015

One-loop matching for transversity generalized parton distribution
journal, September 2015

Transverse momentum dependent parton quasidistributions
journal, June 2019

Axial-vector form factors of the nucleon from lattice QCD
journal, December 2017

Parton distributions from high-precision collider data: NNPDF Collaboration
journal, October 2017

Parton Physics on a Euclidean Lattice
journal, June 2013

Extracting parton distribution functions from lattice QCD calculations
journal, October 2018

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

One-loop matching for parton distributions: Nonsinglet case
journal, July 2014

Quasi-parton distribution functions: A study in the diquark spectator model
journal, April 2015

Renormalizability of quasiparton distribution functions
journal, November 2017

Gluon helicity $Δ G$ from a universality class of operators on a lattice
journal, April 2014

QCD constraints on the shape of polarized quark and gluon distributions
journal, May 1995

Highly improved staggered quarks on the lattice with applications to charm physics
journal, March 2007

Light-Cone Parton Distribution Functions from Lattice QCD
journal, September 2018

Pion distribution amplitude from lattice QCD
journal, May 2017

Soft factor subtraction and transverse momentum dependent parton distributions on the lattice
journal, April 2015

Experimental determination of the π meson structure functions by the Drell-Yan mechanism
journal, December 1983

One-loop evolution of parton pseudo-distribution functions on the lattice
journal, July 2018

Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion
journal, December 2010

Neutron Electric Dipole Moment and Tensor Charges from Lattice QCD
journal, November 2015

Solving the Bars-Green equation for moving mesons in two-dimensional QCD
journal, November 2017

Origin of difference between u ¯ and d ¯ partons in the nucleon
journal, March 1994

Lattice calculation of parton distributions
journal, July 2015

Structure functions of pseudoscalar mesons in the SU(3) NJL model
journal, March 1995

Gaussian-weighted parton quasi-distribution (Lattice Parton Physics Project (LP3))
journal, April 2019

Pion distribution amplitude from Euclidean correlation functions
journal, March 2018

Lattice QCD ensembles with four flavors of highly improved staggered quarks
journal, March 2013

Pion parton distribution function in the valence region
journal, December 2005

Nonperturbative evolution of parton quasi-distributions
journal, April 2017

Deep-inelastic structure function of the pion in the null-plane phenomenology
journal, July 1994

Improved quasi parton distribution through Wilson line renormalization
journal, February 2017

Angular distributions of muon pairs produced by negative pions on deuterium and tungsten
journal, December 1988

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

Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model
journal, December 2017

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

Lattice corrections to the quark quasidistribution at one loop
journal, May 2017

Nucleon and pion distribution functions in the valence region
journal, October 2010

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

Note on lattice regularization and equal-time correlators for parton distribution functions
journal, July 2017

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

One-loop matching for generalized parton distributions
journal, July 2015

Light-cone distribution amplitudes of vector meson in a large momentum effective theory
journal, June 2018

Pion and Nucleon Structure Functions near $x = 1$
journal, November 1975

Pion and kaon valence-quark parton distribution functions
journal, June 2011

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

Nonperturbative partonic quasidistributions of the pion from chiral quark models
journal, October 2017

Matching the quasiparton distribution in a momentum subtraction scheme
journal, March 2018

Valence-quark distribution functions in the kaon and pion
journal, April 2016

Quasi parton distributions and the gradient flow
journal, March 2017

Valence-quark distributions in the pion
journal, January 2001

Quasidistribution amplitude of heavy quarkonia
journal, November 2016