Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD

Jang, Yong-Chull; Gupta, Rajan; Lin, Huey-Wen; Yoon, Boram; Bhattacharya, Tanmoy

doi:10.1103/PhysRevD.101.014507

Title: Nucleon electromagnetic form factors in the continuum limit from ( $2 + 1 + 1$ )-flavor lattice QCD

Abstract

We present results for the isovector (p–n) electromagnetic form factors of the nucleon using 11 ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark action with 2+1+1 dynamical flavors. These ensembles span four lattice spacings a ≈ 0.06, 0.09, 0.12 and 0.15 fm and three values of the light-quark masses corresponding to the pion masses M_π ≈ 135, 225 and 315 MeV. High-statistics estimates using the truncated-solver method allow us to quantify various systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. We analyze the Q² dependence of the form factors calculated over the range 0.05 ≲ Q² ≲ 1.4 GeV² using both the model-independent z expansion and the dipole Ansatz. Our final estimates, using the z-expansion fit, for the isovector root-mean-square radius of nucleon are r_E = 0.769(27)(30) fm, r_M = 0.671(48)(76) fm and μ^p–n = 3.939(86)(138) Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading-order chiral-continuum-finite-volume fits. The estimates from the dipole Ansatz, r_E = 0.765(11)(8) fm, r_M = 0.704(21)(29) fm an μ^p–n = 3.975(84)(125) Bohr magneton, are consistent with those from the z expansion but with smaller errors. Our analysis highlights three points. First, all our data for form factors from the 11 ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapse more clearly onto a single curve when plotted versus Q²/M$$^2_N$$ as compared to Q² with the scale set by quantities other than MN. Here, the difference between these two ways of analyzing the data is indicative of discretization errors, some of which presumably cancel when the data are plotted versus Q²/M$$^2_N$$. Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates for < r$$^2_E$$ >, < r$$^2_M$$ > and μ, high–statistics data for Q² < 0.1 GeV² are needed.

Authors:

Jang, Yong-Chull;

; Lin, Huey-Wen; Yoon, Boram;

; PNDME Collaboration

Publication Date:: 2020-01-23

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division; USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

Contributing Org.:: PNDME Collaboration

OSTI Identifier:: 1593500

Alternate Identifier(s):: OSTI ID: 1599034

Report Number(s):: LA-UR-19-25275
Journal ID: ISSN 2470-0010; PRVDAQ; 014507

Grant/Contract Number:: 89233218CNA000001; AC02-05CH11231; AC05-00OR22725; AC52-06NA25396; PHY 1653405

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; atomic; nuclear and particle physics; nucleon form factors; lattice QCD; charge radii

Citation Formats


                    Jang, Yong-Chull, Gupta, Rajan, Lin, Huey-Wen, Yoon, Boram, Bhattacharya, Tanmoy, and PNDME Collaboration. Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.014507.

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                    Jang, Yong-Chull, Gupta, Rajan, Lin, Huey-Wen, Yoon, Boram, Bhattacharya, Tanmoy, & PNDME Collaboration. Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.101.014507

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                    Jang, Yong-Chull, Gupta, Rajan, Lin, Huey-Wen, Yoon, Boram, Bhattacharya, Tanmoy, and PNDME Collaboration. Thu .  
"Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.101.014507.

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@article{osti_1593500,

  title        = {Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD},

  author       = {Jang, Yong-Chull and Gupta, Rajan and Lin, Huey-Wen and Yoon, Boram and Bhattacharya, Tanmoy and PNDME Collaboration},

  abstractNote = {We present results for the isovector (p–n) electromagnetic form factors of the nucleon using 11 ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quark action with 2+1+1 dynamical flavors. These ensembles span four lattice spacings a ≈ 0.06, 0.09, 0.12 and 0.15 fm and three values of the light-quark masses corresponding to the pion masses Mπ ≈ 135, 225 and 315 MeV. High-statistics estimates using the truncated-solver method allow us to quantify various systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. We analyze the Q2 dependence of the form factors calculated over the range 0.05 ≲ Q2 ≲ 1.4 GeV2 using both the model-independent z expansion and the dipole Ansatz. Our final estimates, using the z-expansion fit, for the isovector root-mean-square radius of nucleon are rE = 0.769(27)(30) fm, rM = 0.671(48)(76) fm and μp–n = 3.939(86)(138) Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading-order chiral-continuum-finite-volume fits. The estimates from the dipole Ansatz, rE = 0.765(11)(8) fm, rM = 0.704(21)(29) fm an μp–n = 3.975(84)(125) Bohr magneton, are consistent with those from the z expansion but with smaller errors. Our analysis highlights three points. First, all our data for form factors from the 11 ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapse more clearly onto a single curve when plotted versus Q2/M$^2_N$ as compared to Q2 with the scale set by quantities other than MN. Here, the difference between these two ways of analyzing the data is indicative of discretization errors, some of which presumably cancel when the data are plotted versus Q2/M$^2_N$. Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates for < r$^2_E$ >, < r$^2_M$ > and μ, high–statistics data for Q2 < 0.1 GeV2 are needed.},

  doi          = {10.1103/PhysRevD.101.014507},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 101,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Non-singlet axial vector couplings of the baryon octet in lattice QCD
journal, August 1989

Güsken, S.; Löw, U.; Mütter, K. -H.
Physics Letters B, Vol. 227, Issue 2
DOI: 10.1016/S0370-2693(89)80034-6

Isovector charges of the nucleon from $2 + 1 + 1$ -flavor lattice QCD
journal, August 2018

Gupta, Rajan; Jang, Yong-Chull; Yoon, Boram
Physical Review D, Vol. 98, Issue 3
DOI: 10.1103/PhysRevD.98.034503

Measurements of Neutron Form Factors
journal, March 1966

Stein, P.; Binkley, M.; McAllister, R.
Physical Review Letters, Vol. 16, Issue 13
DOI: 10.1103/PhysRevLett.16.592

Precise measurements of the neutron magnetic form factor
journal, June 1998

Anklin, H.; deBever, L. J.; Blomqvist, K. I.
Physics Letters B, Vol. 428, Issue 3-4
DOI: 10.1016/S0370-2693(98)00442-0

The Chroma Software System for Lattice QCD
journal, March 2005

Edwards, Robert G.; Joó, Bálint
Nuclear Physics B - Proceedings Supplements, Vol. 140
DOI: 10.1016/j.nuclphysbps.2004.11.254

Nucleon electromagnetic form factors
journal, May 2007

Arrington, J.; Roberts, C. D.; Zanotti, J. M.
Journal of Physics G: Nuclear and Particle Physics, Vol. 34, Issue 7
DOI: 10.1088/0954-3899/34/7/s03

Proton and neutron electromagnetic form factors from lattice QCD
text, January 2018

Alexandrou, C.; Bacchio, S.; Constantinou, M.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-00443

Works referencing / citing this record:

Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation
journal, February 2020

Jang, Yong-Chull; Gupta, Rajan; Yoon, Boram
Physical Review Letters, Vol. 124, Issue 7
DOI: 10.1103/physrevlett.124.072002

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Title: Nucleon electromagnetic form factors in the continuum limit from ( 2 + 1 + 1 )-flavor lattice QCD

Abstract

Citation Formats

Measurement of G E p / G M p in e → p → e p → to Q 2 = 5.6 GeV 2 journal, February 2002

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Measurement of the Electric Form Factor of the Neutron through d → ( e → , e ′ n ) p at Q 2 = 0.5 ( GeV / c ) 2 journal, August 2001

Electric and magnetic form factors of the proton journal, July 2014

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

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New class of variance-reduction techniques using lattice symmetries journal, November 2013

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Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator journal, November 2010

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Measurement of the magnetic form factor of the neutron journal, July 1993

Measurement of the neutron magnetic form factor from inclusive quasielastic scattering of polarized electrons from polarized He 3 journal, August 1994

Robust extraction of the proton charge radius from electron-proton scattering data journal, August 2018

Nucleon electromagnetic form factors journal, October 2007

Measurement of the Neutron Electric Form Factor G en at 0.67 ( GeV / c ) 2 via 3 He → ( e → , e ′ n ) journal, November 1999

Measurement of the Neutron Electric Form Factor G E , n in the Quasifree H 2 ( e → , e ′ n → ) p Reaction journal, July 1999

Nucleon properties at finite lattice spacing in chiral perturbation theory journal, December 2003

Reexamination of proton rms radii from low- q power expansions journal, January 2017

Computing the nucleon charge and axial radii directly at Q 2 = 0 in lattice QCD journal, February 2018

Review of Particle Physics journal, August 2018

Large-Angle Quasielastic Electron-Deuteron Scattering journal, August 1973

Defining the proton radius: A unified treatment journal, March 2019

Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding journal, June 1999

Proton root-mean-square radii and electron scattering journal, January 2014

CODATA recommended values of the fundamental physical constants: 2014 journal, September 2016

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

Neutron charge form factor at large q 2 journal, September 2001

Simple parametrization of nucleon form factors journal, December 2004

Model-independent determination of the axial mass parameter in quasielastic neutrino-nucleon scattering journal, October 2011

Nucleon form factors and root-mean-square radii on a ( 10.8 fm ) 4 lattice at the physical point journal, January 2019

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

Nucleon electromagnetic form factors in two-flavor QCD journal, September 2015

Model-independent extraction of the proton charge radius from electron scattering journal, December 2010

Electromagnetic form factors of the neutron at squared four-momentum transfers of 1.0 and 1.5 (GeV/c)2 journal, May 1972

First measurement of the electric formfactor of the neutron in the exclusive quasielastic scattering of polarized electrons from polarized 3He journal, May 1994

Extraction of the neutron magnetic form factor from quasielastic 3 He → ( e → , e ' ) at Q 2 = 0.1 − 0.6 ( GeV / c ) 2 journal, March 2007

Proton elastic form factor ratios to Q 2 = 3.5 GeV 2 by polarization transfer journal, May 2005

Precise neutron magnetic form factors journal, January 2002

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 electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆ journal, January 2005

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Extraction of the proton radius from electron-proton scattering data journal, July 2015

Lattice QCD with a chirally twisted mass term journal, August 2001

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

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

The neutron charge form factor and target analyzing powers from 3He(e→,e′n) scattering journal, July 2003

Low-energy analysis of the nucleon electromagnetic form factors journal, January 2001

Nucleon electromagnetic form factors on the lattice and in chiral effective field theory journal, February 2005

Proton and neutron electromagnetic form factors and uncertainties journal, February 2018

Electric form factor of the neutron from the H 2 ( e →, e ’ n → ) 1 H reaction at Q 2 =0.255 (GeV/ c ) 2 journal, October 1994

High-Precision Determination of the Electric and Magnetic Form Factors of the Proton journal, December 2010

Measurement of the Neutron Magnetic Form Factor journal, July 1995

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Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries journal, December 2017

Nucleon electromagnetic form factors using lattice simulations at the physical point journal, August 2017

Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass journal, June 2019

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The Proton Form Factor Ratio Measurements at Jefferson Lab journal, January 2014

Neutron Form Factors from Quasi-Elastic Electron-Deuteron Scattering journal, September 1968

Proton and neutron electromagnetic form factors from lattice QCD journal, July 2019

Nucleon structure from mixed action calculations using 2 + 1 flavors of asqtad sea and domain wall valence fermions journal, November 2010

Charge Form Factor of the Neutron from the Reaction 2 H → ( e → , e ′ n ) p journal, June 1999

Neutron charge radius and the neutron electric form factor journal, May 2011

Controlling excited-state contamination in nucleon matrix elements journal, June 2016

Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized 3 He target journal, February 2001

Measurement of the Electric Form Factor of the Neutron at Q 2 = 0.5 and 1.0 G e V 2 / c 2 journal, January 2004

Isovector charges of the nucleon from 2 + 1 -flavor QCD with clover fermions journal, April 2017

Title: Nucleon electromagnetic form factors in the continuum limit from ( $2 + 1 + 1$ )-flavor lattice QCD

Measurement of $G_{E_{p}} / G_{M_{p}}$ in $\vec{e} p \to e \vec{p}$ to $Q^{2} = 5.6 {GeV}^{2}$
journal, February 2002

Effective noise reduction techniques for disconnected loops in Lattice QCD
journal, September 2010

Nucleon form factors on a large volume lattice near the physical point in $2 + 1$ flavor QCD
journal, October 2018

On the discretization of physical momenta in lattice QCD
journal, August 2004

Measurements of the neutron electric to magnetic form factor ratio $G_{En} / G_{Mn}$ via the ${}^{2}H$ $(\vec{e}, e^{'} \vec{n})$ ${}^{1}H$ reaction to $Q^{2} = 1.45$ (GeV/ $c)^{2}$
journal, February 2006

Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
journal, October 2014

Review of Particle Physics
journal, October 2016

Precision measurement of the neutron magnetic form factor
journal, September 1994

Measurement of the Electric Form Factor of the Neutron through $\vec{d} (\vec{e}, e^{'} n) p$ at $Q^{2} = 0.5 (GeV / c)^{2}$
journal, August 2001

Electric and magnetic form factors of the proton
journal, July 2014

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

Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
journal, March 2017

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

New class of variance-reduction techniques using lattice symmetries
journal, November 2013

Axial, scalar, and tensor charges of the nucleon from $2 + 1 + 1$ -flavor Lattice QCD
journal, September 2016

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
journal, November 2010

High-precision calculation of the strange nucleon electromagnetic form factors
journal, August 2015

Publisher's Note: Proton elastic form factor ratios to $Q^{2} = 3.5 {GeV}^{2}$ by polarization transfer [Phys. Rev. C 71, 055202 (2005)]
journal, June 2005

Measurement of the magnetic form factor of the neutron
journal, July 1993

Measurement of the neutron magnetic form factor from inclusive quasielastic scattering of polarized electrons from polarized ${}^{3}{He}$
journal, August 1994

Robust extraction of the proton charge radius from electron-proton scattering data
journal, August 2018

Nucleon electromagnetic form factors
journal, October 2007

Measurement of the Neutron Electric Form Factor $G_{en}$ at $0.67 (GeV / c) 2$ via $^{3} \vec{He} (\vec{e}, e^{'} n)$
journal, November 1999

Measurement of the Neutron Electric Form Factor $G_{E, n}$ in the Quasifree ${}^{2}H (\vec{e}, e^{'} \vec{n}) p$ Reaction
journal, July 1999

Nucleon properties at finite lattice spacing in chiral perturbation theory
journal, December 2003

Reexamination of proton rms radii from low- $q$ power expansions
journal, January 2017

Computing the nucleon charge and axial radii directly at $Q^{2} = 0$ in lattice QCD
journal, February 2018

Review of Particle Physics
journal, August 2018

Large-Angle Quasielastic Electron-Deuteron Scattering
journal, August 1973

Defining the proton radius: A unified treatment
journal, March 2019

Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding
journal, June 1999

Proton root-mean-square radii and electron scattering
journal, January 2014

CODATA recommended values of the fundamental physical constants: 2014
journal, September 2016

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

Neutron charge form factor at large $q^{2}$
journal, September 2001

Simple parametrization of nucleon form factors
journal, December 2004

Model-independent determination of the axial mass parameter in quasielastic neutrino-nucleon scattering
journal, October 2011

Nucleon form factors and root-mean-square radii on a ${(10.8 fm)}^{4}$ lattice at the physical point
journal, January 2019

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

Nucleon electromagnetic form factors in two-flavor QCD
journal, September 2015

Model-independent extraction of the proton charge radius from electron scattering
journal, December 2010

Electromagnetic form factors of the neutron at squared four-momentum transfers of 1.0 and 1.5 (GeV/c)2
journal, May 1972

First measurement of the electric formfactor of the neutron in the exclusive quasielastic scattering of polarized electrons from polarized 3He
journal, May 1994

Extraction of the neutron magnetic form factor from quasielastic $^{3} \vec{He}$ ( $\vec{e}, e^{'}$ ) at $Q^{2} = 0.1 − 0.6 (GeV / c)^{2}$
journal, March 2007

Proton elastic form factor ratios to $Q^{2} = 3.5 GeV^{2}$ by polarization transfer
journal, May 2005

Precise neutron magnetic form factors
journal, January 2002

Measurements of $G_{E}^{n} / G_{M}^{n}$ from the ${}^{2}H (\vec{e}, e^{'} \vec{n}) {}^{1}H$ Reaction to $Q^{2} = 1.45$ $(G e V / c)^{2}$
journal, September 2003

Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆
journal, January 2005

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Extraction of the proton radius from electron-proton scattering data
journal, July 2015

Lattice QCD with a chirally twisted mass term
journal, August 2001

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

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

The neutron charge form factor and target analyzing powers from 3He(e→,e′n) scattering
journal, July 2003

Low-energy analysis of the nucleon electromagnetic form factors
journal, January 2001

Nucleon electromagnetic form factors on the lattice and in chiral effective field theory
journal, February 2005

Proton and neutron electromagnetic form factors and uncertainties
journal, February 2018

Electric form factor of the neutron from the ${}^{2}H$ ( e →, $e^{’}$ n → $)^{1}$ H reaction at $Q^{2}$ =0.255 (GeV/ c $)^{2}$
journal, October 1994

High-Precision Determination of the Electric and Magnetic Form Factors of the Proton
journal, December 2010

Measurement of the Neutron Magnetic Form Factor
journal, July 1995

Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
journal, April 2019

Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen
journal, January 2013

The form factors of the nucleon at small momentum transfer
journal, May 1998

Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries
journal, December 2017

Nucleon electromagnetic form factors using lattice simulations at the physical point
journal, August 2017

Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass
journal, June 2019

Experiments towards resolving the proton charge radius puzzle
journal, January 2016

The Proton Form Factor Ratio Measurements at Jefferson Lab
journal, January 2014

Neutron Form Factors from Quasi-Elastic Electron-Deuteron Scattering
journal, September 1968

Proton and neutron electromagnetic form factors from lattice QCD
journal, July 2019

Nucleon structure from mixed action calculations using $2 + 1$ flavors of asqtad sea and domain wall valence fermions
journal, November 2010

Charge Form Factor of the Neutron from the Reaction $^{2} \vec{H} (\vec{e}, e^{'} n) p$
journal, June 1999

Neutron charge radius and the neutron electric form factor
journal, May 2011

Controlling excited-state contamination in nucleon matrix elements
journal, June 2016

Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on a polarized $^{3} He$ target
journal, February 2001

Measurement of the Electric Form Factor of the Neutron at $Q^{2} = 0.5$ and $1.0 {G e V}^{2} / c^{2}$
journal, January 2004

Isovector charges of the nucleon from $2 + 1$ -flavor QCD with clover fermions
journal, April 2017

Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c)2
journal, July 1973

Non-singlet axial vector couplings of the baryon octet in lattice QCD
journal, August 1989