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

Krzysztof Cichy,Martha Constantinou

doi:10.1155/2019/3036904

Abstract

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.

Highlights

Among the frontiers of nuclear and particle physics is the investigation of the structure of hadrons, the architecture elements of the visible matter
If it is too large, periodicity of the Fourier transform will induce nonphysical oscillations in the quasi-parton distribution functions (PDFs), especially at large x. We note that these oscillations do not appear because of the truncation at finite zmax, but rather because of a too large value of zmax at low momenta. This effect can be naturally suppressed by simulating at larger nucleon boosts and as we show in Section 9, oscillations are dampened at larger P3
We review other results obtained with the quasidistribution method, for mesonic Distribution amplitude deep-inelastic scattering (DIS) (DA) and PDFs, as well as first exploratory results for gluon PDFs

Summary

Introduction

Among the frontiers of nuclear and particle physics is the investigation of the structure of hadrons, the architecture elements of the visible matter. Hadrons consist of quarks and gluons (together called partons), which are governed by one of the four fundamental forces of nature, the strong force. The latter is described by the theory of Quantum Chromodynamics (QCD). Understanding QCD can have great impact on many aspects of science, from the subnuclear interactions to astrophysics, and, a quantitative description is imperative. This is a very challenging task, as QCD is a highly nonlinear theory. An ideal ab initio formulation is Lattice QCD, a spacetime discretization of the theory that allows the study of the properties of fundamental particles numerically, starting from the original QCD Lagrangian

Objectives

Results

Conclusion