Abstract
Quasi and pseudo distributions provide a new approach to determining parton distribution functions (PDFs) from first principles' calculations of quantum chromodynamics (QCD). Here I calculate the flavor nonsinglet unpolarized quasi distribution at one loop in perturbation theory, using the gradient flow to remove ultraviolet divergences. I demonstrate that, as expected, the gradient flow does not change the infrared structure of the quasi distribution at one loop and use the results to match the smeared matrix elements to those in the $\ms$ scheme. This matching calculation is required to relate numerical results obtained from nonperturbative lattice QCD computations to light-front PDFs extracted from global analyses of experimental data.
Highlights
A central challenge for QCD, the gauge theory of the strong nuclear force, is the direct prediction of hadron structure
In Ref. [25], we introduced an alternative approach, the smeared quasidistribution, which circumvents some of the challenges of the power divergence by taking advantage of the properties of the gradient flow [26,27,28]
Quasi- and pseudodistributions have opened a new window into nucleon structure and provided an opportunity to extract, for the first time, parton distribution functions directly from lattice QCD
Summary
A central challenge for QCD, the gauge theory of the strong nuclear force, is the direct prediction of hadron structure. Ab initio determination of PDFs and GPDs has yet to appear, a promising new method was recently proposed in Ref. In this approach, PDFs and GPDs are extracted from matrix elements of spatially extended operators between nucleon states at finite momentum. PDFs and GPDs are extracted from matrix elements of spatially extended operators between nucleon states at finite momentum These matrix elements are generally referred to as quasi-PDFs or quasidistributions. Related frameworks have been proposed; in Refs. [2,3,4], quasidistributions were treated as “lattice cross sections” from which light-front PDFs can be factorized, and Refs. Related frameworks have been proposed; in Refs. [2,3,4], quasidistributions were treated as “lattice cross sections” from which light-front PDFs can be factorized, and Refs. [5,6,7] introduced and studied the closely related pseudodistributions
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