scholarly journals A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

2019 ◽  
Vol 2019 ◽  
pp. 1-68 ◽  
Author(s):  
Krzysztof Cichy ◽  
Martha Constantinou

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.

2018 ◽  
Vol 121 (11) ◽  
Author(s):  
Constantia Alexandrou ◽  
Krzysztof Cichy ◽  
Martha Constantinou ◽  
Karl Jansen ◽  
Aurora Scapellato ◽  
...  

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Markus A. Ebert ◽  
Bernhard Mistlberger ◽  
Gherardo Vita

Abstract We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Luigi Del Debbio ◽  
Tommaso Giani ◽  
Joseph Karpie ◽  
Kostas Orginos ◽  
Anatoly Radyushkin ◽  
...  

Abstract We extract two nonsinglet nucleon Parton Distribution Functions from lattice QCD data for reduced Ioffe-time pseudodistributions. We perform such analysis within the NNPDF framework, considering data coming from different lattice ensembles and dis- cussing in detail the treatment of the different source of systematics involved in the fit. We introduce a recipe for taking care of systematics and use it to perform our extraction of light-cone PDFs.


2012 ◽  
Author(s):  
Michael Engelhardt ◽  
Bernhard Musch ◽  
Philipp Haegler ◽  
John Negele ◽  
Andreas Schafer

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Alessandro Candido ◽  
Stefano Forte ◽  
Felix Hekhorn

Abstract It is common lore that Parton Distribution Functions (PDFs) in the $$ \overline{\mathrm{MS}} $$ MS ¯ factorization scheme can become negative beyond leading order due to the collinear subtraction which is needed in order to define partonic cross sections. We show that this is in fact not the case and next-to-leading order (NLO) $$ \overline{\mathrm{MS}} $$ MS ¯ PDFs are actually positive in the perturbative regime. In order to prove this, we modify the subtraction prescription, and perform the collinear subtraction in such a way that partonic cross sections remain positive. This defines a factorization scheme in which PDFs are positive. We then show that positivity of the PDFs is preserved when transforming from this scheme to $$ \overline{\mathrm{MS}} $$ MS ¯ , provided only the strong coupling is in the perturbative regime, such that the NLO scheme change is smaller than the LO term.


2013 ◽  
Author(s):  
Michael Engelhardt ◽  
Bernhard Musch ◽  
Philipp Haegler ◽  
John Negele ◽  
Andreas Schafer

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 205-208
Author(s):  
JOEY HUSTON

This talk is intended to serve as a pedagogical guide on the determination of, the proper use of, and the uncertainties of parton distribution functions and their impact on physics cross sections at the Tevatron and LHC. A longer writeup of this talk is available at .


2015 ◽  
Vol 56 (6-9) ◽  
pp. 447-453 ◽  
Author(s):  
M. Engelhardt ◽  
B. Musch ◽  
P. Hägler ◽  
J. Negele ◽  
A. Schäfer

2003 ◽  
Vol 18 (38) ◽  
pp. 2681-2697 ◽  
Author(s):  
W. DETMOLD ◽  
W. MELNITCHOUK ◽  
A. W. THOMAS

We review the calculation of moments of both the polarized and unpolarized parton distribution functions of the nucleon in lattice QCD, and in particular their extrapolation to the physical region. We also discuss the reconstruction of the x dependence of the valence quark distributions in the nucleon from a finite number of lattice moments.


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