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Title: Charting the coming synergy between lattice QCD and high-energy phenomenology

Abstract

Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions (PDFs), such as $$\langle x \rangle_{u^+ - d^+}$$ and $$\langle x \rangle_{g}$$, as well as $x$-dependent quark quasi-distributions --- in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleon's collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.

Authors:
 [1];  [2];  [2];  [2]
  1. Southern Methodist Univ., Dallas, TX (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Southern Methodist Univ., Dallas, TX (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1575963
Alternate Identifier(s):
OSTI ID: 1576228
Report Number(s):
JLAB-PHY-19-3038; DOE/OR/23177-4854; arXiv:1904.00022
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
SC0010129; AC05-06OR23177
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 100; Journal Issue: 9; 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

Hobbs, Timothy J., Wang, Bo -Ting, Nadolsky, Pavel, and Olness, Fredrick I. Charting the coming synergy between lattice QCD and high-energy phenomenology. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.094040.
Hobbs, Timothy J., Wang, Bo -Ting, Nadolsky, Pavel, & Olness, Fredrick I. Charting the coming synergy between lattice QCD and high-energy phenomenology. United States. doi:10.1103/PhysRevD.100.094040.
Hobbs, Timothy J., Wang, Bo -Ting, Nadolsky, Pavel, and Olness, Fredrick I. Wed . "Charting the coming synergy between lattice QCD and high-energy phenomenology". United States. doi:10.1103/PhysRevD.100.094040.
@article{osti_1575963,
title = {Charting the coming synergy between lattice QCD and high-energy phenomenology},
author = {Hobbs, Timothy J. and Wang, Bo -Ting and Nadolsky, Pavel and Olness, Fredrick I.},
abstractNote = {Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions (PDFs), such as $\langle x \rangle_{u^+ - d^+}$ and $\langle x \rangle_{g}$, as well as $x$-dependent quark quasi-distributions --- in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleon's collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.},
doi = {10.1103/PhysRevD.100.094040},
journal = {Physical Review D},
number = 9,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.094040

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Works referenced in this record:

Strange asymmetries in the nucleon sea
journal, April 1999


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


Extraction of Parton Distributions from Lattice qcd
journal, December 2003


Measurement of the inclusive jet cross section at the Fermilab Tevatron p p ¯ collider using a cone-based jet algorithm
journal, September 2008


Measurement of forward W and Z boson production in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeV
journal, January 2016

  • Aaij, R.; Abellán Beteta, C.; Adeva, B.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)155

Pion cloud of the nucleon and its effect on deep-inelastic structure
journal, May 1992


Gottfried sum from the ratio F 2 n / F 2 p
journal, May 1991


Measurement of inclusive jet and dijet production in p p collisions at s = 7 TeV using the ATLAS detector
journal, July 2012


Improved Determination of α s From Neutrino-Nucleon Scattering
journal, August 1997


Measurement of the Electron Charge Asymmetry in Inclusive W Production in p p Collisions at s = 7 TeV
journal, September 2012


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


Measurements of differential jet cross sections in proton-proton collisions at s = 7 TeV with the CMS detector
journal, June 2013


Measurement of the proton and deuteron structure functions, F2p and F2d, and of the ratio
journal, January 1997


The moment x u d of the nucleon from N f = 2 lattice QCD down to nearly physical quark masses
journal, October 2014


Moments of nucleon light cone quark distributions calculated in full lattice QCD
journal, August 2002


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


Transverse momentum dependent distribution functions in the bag model
journal, April 2010


Taming the Pion Cloud of the Nucleon
journal, April 2012


Parton distributions in the LHC era: MMHT 2014 PDFs
journal, May 2015


Non-Lagrangian Models of Current Algebra
journal, March 1969


New Generation of Parton Distributions with Uncertainties from Global QCD Analysis
journal, July 2002


Asymptotically Free Gauge Theories. I
journal, November 1973


The structure of the proton in the LHC precision era
journal, May 2018


First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function
journal, August 2019


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


Mapping the sensitivity of hadronic experiments to nucleon structure
journal, November 2018


Measurement of the Z/γ * boson transverse momentum distribution in pp collisions at s = 7 $$ \sqrt{s}=7 $$ TeV with the ATLAS detector
journal, September 2014

  • Aad, G.; Abbott, B.; Abdallah, J.
  • Journal of High Energy Physics, Vol. 2014, Issue 9
  • DOI: 10.1007/JHEP09(2014)145

CTEQ-TEA parton distribution functions and HERA Run I and II combined data
journal, February 2017


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


Phenomenology of nonperturbative charm in the nucleon
journal, April 2014


Combination and QCD analysis of charm production cross section measurements in deep-inelastic ep scattering at HERA
journal, February 2013


Dimuon production in proton-copper collisions at s = 38.8 GeV
journal, May 1991


Flavor asymmetry of antiquark distributions in the nucleon
journal, September 1998


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


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


Experimental consistency in parton distribution fitting
journal, April 2010


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


Pion valence quark distribution from matrix element calculated in lattice QCD
journal, April 2019


Physics opportunities of a fixed-target experiment using LHC beams
journal, January 2013


A high statistics measurement of the proton structure functions F2(x, Q2) and R from deep inelastic muon scattering at high Q2
journal, June 1989


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


Nucleon isovector structure functions in ( 2 + 1 )-flavor QCD with domain wall fermions
journal, July 2010


Higher twist contributions to the structure functions <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:msubsup><mml:mi>F</mml:mi><mml:mn>2</mml:mn><mml:mi>p</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>Q</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math altimg="si2.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:msubsup><mml:mi>F</mml:mi><mml:mn>2</mml:mn><mml:mi>d</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mi>Q</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math> at large x at higher orders
journal, May 2008


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


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

Measurement of the forward-backward charge asymmetry from W e ν production in p p ¯ collisions at s = 1.96     TeV
journal, March 2005


Forward-Backward Charge Asymmetry of Electron Pairs above the Z 0 Pole
journal, September 1996


Measurement of the double-differential high-mass Drell-Yan cross section in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeV with the ATLAS detector
journal, August 2016

  • Aad, G.; Abbott, B.; Abdallah, J.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)009

Inclusive W and Z production in the forward region at $ \sqrt {s} = 7\,{\text{TeV}} $
journal, June 2012

  • Aaij, R.; Abellan Beteta, C.; Adametz, A.
  • Journal of High Energy Physics, Vol. 2012, Issue 6
  • DOI: 10.1007/JHEP06(2012)058

Nucleon Spin and Momentum Decomposition Using Lattice QCD Simulations
journal, October 2017


Uncertainties of predictions from parton distribution functions. I. The Lagrange multiplier method
journal, December 2001


Measurement of the forward Z boson production cross-section in pp collisions at s = 7 $$ \sqrt{s}=7 $$ TeV
journal, August 2015

  • Aaij, R.; Adeva, B.; Adinolfi, M.
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)039

Parton distribution functions in the pion from lattice QCD
journal, August 2003


Uncertainties of predictions from parton distribution functions. II. The Hessian method
journal, December 2001


d ¯ u ¯ Asymmetry in the Proton in Chiral Effective Theory
journal, March 2015


A high statistics measurement of the deuteron structure functions F2(x, Q2) and R from deep inelastic muon scattering at high Q2
journal, March 1990


Lattice operators for moments of the structure functions and their transformation under the hypercubic group
journal, November 1996


Constraining nucleon strangeness
journal, March 2015


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


Parton Physics on a Euclidean Lattice
journal, June 2013


Bayesian analysis of light-front models and the nucleon’s charmed sigma term
journal, October 2017


Asymptotically free gauge theories. II
journal, February 1974


Improved measurement of the d ¯ / ū asymmetry in the nucleon sea
journal, August 2001


Nucleon quark distribution functions from the Dyson–Schwinger equations
journal, July 2018


Measurement of the electron charge asymmetry in p p ¯ W + X e ν + X decays in p p ¯ collisions at s = 1.96 TeV
journal, February 2015


A statistical approach for polarized parton distributions
journal, April 2002

  • Bourrely, C.; Soffer, J.; Buccella, F.
  • The European Physical Journal C, Vol. 23, Issue 3
  • DOI: 10.1007/s100520100855

A general method for non-perturbative renormalization of lattice operators
journal, July 1995


A Large Hadron Electron Collider at CERN Report on the Physics and Design Concepts for Machine and Detector
journal, July 2012

  • Abelleira Fernandez, J. L.; Adolphsen, C.; Akay, A. N.
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 39, Issue 7
  • DOI: 10.1088/0954-3899/39/7/075001

Measurement of forward Z → e+e− production at s = 8 $$ \sqrt{s}=8 $$ TeV
journal, May 2015

  • Aaij, R.; Adeva, B.; Adinolfi, M.
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)109

Polarized and unpolarized nucleon structure functions from lattice QCD
journal, March 1996


Freedom at moderate energies: Masses in color dynamics
journal, October 1976


A limit on the pionic component of the nucleon through SU(3) flavour breaking in the sea
journal, June 1983


Reevaluation of the Gottfried sum
journal, July 1994


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


Nucleon structure from Lattice QCD using a nearly physical pion mass
journal, June 2014


Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017


Electroproduction scaling in an asymptotically free theory of strong interactions
journal, January 1974


x and x 2 of the pion PDF from lattice QCD with N f = 2 + 1 + 1 dynamical quark flavors
journal, January 2019


Measurement of the Inclusive Jet Cross Section in p p ¯ Collisions at s = 1.96 TeV
journal, August 2008


A measurement of differential cross-sections and nucleon structure functions in charged-current neutrino interactions on iron
journal, June 1991

  • Berge, P.; Burkhardt, H.; Dydak, F.
  • Zeitschrift f�r Physik C Particles and Fields, Vol. 49, Issue 2
  • DOI: 10.1007/BF01555493

Sum Rule for High-Energy Electron-Proton Scattering
journal, June 1967


Measurement of the muon charge asymmetry from W boson decays
journal, January 2008


Flavor Su(2) Symmetry Breaking in deep Inelastic Scattering
journal, January 1991


Moments of nucleon’s parton distribution for the sea and valence quarks from lattice QCD
journal, May 2009


Measurements of F 2 and xF 3 ν xF 3 ν ¯ from CCFR ν μ -Fe and ν ¯ μ -Fe Data in a Physics Model-Independent Way
journal, March 2001


Light-Cone Behavior of Perturbation Theory
journal, December 1972


Measurement of the inclusive e ± p scattering cross section at high inelasticity y and of the structure function F L
journal, March 2011


Measurement of the ratios of the <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>Z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi>γ</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mo>⩾</mml:mo><mml:mi>n</mml:mi></mml:math> jet production cross sections to the total inclusive <mml:math altimg="si2.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>Z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi>γ</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math> cross section in <mml:math altimg="si3.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>p</mml:mi><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> collisions at <mml:math altimg="si4.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:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1.96</mml:mn><mml:mtext> TeV</mml:mtext></mml:math>
journal, January 2008


Measurement of <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>d</mml:mi><mml:mi>σ</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:math> of Drell–Yan <mml:math altimg="si2.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:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> pairs in the Z mass region from <mml:math altimg="si3.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>p</mml:mi><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> collisions at <mml:math altimg="si4.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:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1.96</mml:mn><mml:mtext> TeV</mml:mtext></mml:math>
journal, September 2010


A lattice determination of moments of unpolarized nucleon structure functions using improved Wilson fermions
journal, June 2005


Parton distributions from lattice QCD
journal, August 2001