TY - JOUR
T1 - A Guide to Light-Cone PDFs from Lattice QCD
T2 - An Overview of Approaches, Techniques, and Results
AU - Cichy, Krzysztof
AU - Constantinou, Martha
AU - Prokudin, Alexei
N1 - Funding Information:
We first want to thank the editors of the special issue "TransverseMomentumDependent Observables fromLow to High Energy: Factorization, Evolution, and Global Analyses" for the invitation to prepare this review and the guidance they provided throughout the process. We are also grateful to all Authors for giving permission for the figures we used to illustrate the progress of the field.We are indebted to several peoplewithwhomwehaddiscussions over the years andwho helped to shape our view on different aspects discussed in this review.Their names are, in alphabetical order, C.Alexandrou, G. Bali, R. Briceño,W. Broniowski, J.-W. Chen, I. C. Cloet,W. Detmold, V. Drach, M. Engelhardt, L. Gamberg, E. García-Ramos, K. Golec-Biernat, J. Green, K. Hadjiyiannakou, K. Jansen, X. Ji, P. Korcyl, G. Koutsou, P. Kotko, K. Kutak, C.-J.D. Lin, K.-F. Liu, S. Liuti, W. Melnitchouk, A. Metz, Z.-E. Meziani, C. Monahan, K. Orginos, H. Panagopoulos, A. Prokudin, J.-W. Qiu, A. Radyushkin, G. C. Rossi, N. Sato, M. Savage, A. Scapellato, R. Sommer, F. Steffens, I. W. Stewart, R. Sufian, J. Wagner, Ch. Wiese, J. Wosiek, Y.-B. Yang, F. Yuan, S. Zafeiropoulos, J.-H. Zhang, and Y. Zhao. We also thank all members of the TMD Topical Collaboration for enlightening discussions. Krzysztof Cichy is supported by the National Science Centre (Poland) Grant SONATA BIS no. 2016/22/E/ST2/00013. Martha Constantinou acknowledges financial support by the U.S. Department of Energy, Office of Nuclear Physics, within the framework of the TMD Topical Collaboration, as well as by the National Science Foundation under Grant no. PHY-1714407.
Funding Information:
Copyright © 2019 Krzysztof Cichy and Martha Constantinou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.
Publisher Copyright:
© 2019 Krzysztof Cichy and Martha Constantinou.
PY - 2019
Y1 - 2019
N2 - Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal nonperturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transverse momentum dependent parton distributions (TMDs), and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice. In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasidistributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasidistribution approach, such as renormalization, matching to light-cone distributions, and lattice techniques. In addition to a thorough discussion of quasidistributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudodistributions, OPE without OPE, and good lattice cross-sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.
AB - Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal nonperturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transverse momentum dependent parton distributions (TMDs), and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice. In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasidistributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasidistribution approach, such as renormalization, matching to light-cone distributions, and lattice techniques. In addition to a thorough discussion of quasidistributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudodistributions, OPE without OPE, and good lattice cross-sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.
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U2 - 10.1155/2019/3036904
DO - 10.1155/2019/3036904
M3 - Review article
AN - SCOPUS:85067684145
VL - 2019
JO - Advances in High Energy Physics
JF - Advances in High Energy Physics
SN - 1687-7357
M1 - 3036904
ER -