On the calculation of parton distributions from Lattice QCD

Abstract

A new method for calculating parton distribution functions from lattice QCD is implemented and studied. Lattice QCD calculable matrix elements with space-like separated fields have an analogous operator product expansion to experimental scattering cross sections and thus these matrix elements are known as "Good Lattice Cross Sections". Using the colinear factorization approach, a Good Lattice Cross Section can be factorized to the short distance matching kernels that are computed in perturbation theory and the non-perturbative parton distribution functions. As a result, using the perturbative matching kernels and the non-perturbatively computed matrix elements, one can obtain the parton distribution functions. The nucleon and pion matrix elements are determined on a set of 2+1 flavors of clover improved quarks with heavier than physical pion mass. The determination of the parton distributions from Good Lattice Cross Sections constitutes an ill-posed inverse problem. Methods for accurate determination of parton distributions from the Good Lattice Cross Sections are studied. With the calculation of several Good Lattice Cross Sections, the determination of the parton distributions can be improved with a simultaneous analysis, similar to the global parton distribution fits to experimental cross sections.

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks

“…However, these approaches introduce uncontrolled systematic errors. A straightforward example of a stable solution to the inverse problem, which was used in [8,12], is to parametrize the solution with a functional form, such as (1.4), containing a small number of parameters. One can then use this functional form to fit the data using a χ 2 minimization.…”

Recent Developments in $x$-dependent Structure Calculations

“…Pseudo PDFs The first unquenched results for pseudo PDFs appear in [47], which I show in the left hand plot in Fig. 5.…”

“…Perhaps the most challenging systematic uncertainty for this entire approach, then, is the spurious oscillations introduced by the Fourier transform of the matrix element. A number of approaches have been proposed to overcome this challenge, including a low-pass filter, the "derivative method", and Gaussian weighting for quasi PDFs [46] (see also [12]) and Backus-Gilbert, Bayesian and neural network reconstruction for pseudo PDFs [47]. It is not yet clear, however, if these oscillations can be completely controlled in a model independent way [5].…”

“…(Left) The reduced Ioffe time matrix element from[47]. (Right) The heavy-light hadronic tensor from[71].…”

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

“…Further progress was reported in the Lattice 2018 Symposium, including first calculations with dynamical flavors [257] and the issue of reconstruction of distributions from a limited set of data 12 . FIG.…”