Partonic quasidistributions in two-dimensional QCD

TL;DR

This paper compares quasi and light-cone parton distributions in two-dimensional QCD, employing an operator approach with a soft cutoff, revealing how quasi distributions approach light-cone distributions as meson momentum increases.

Contribution

It introduces a Hamiltonian operator method with a soft momentum cutoff to derive and compare quasi and light-cone distributions in the 't Hooft model, providing new insights into their IR behavior and approach rate.

Findings

Quasi distributions approach light-cone distributions more slowly for light mesons than for heavy quarkonia.

Both quasi and light-cone PDFs share the same IR behavior at leading order in 1/P^z.

The operator approach with a soft cutoff effectively reconstructs the 't Hooft and Bars-Green equations.

Abstract

As a sequel of our preceding work [1] we carry out a comprehensive comparative study between the quasi parton distribution functions (PDFs), distribution amplitudes (DAs) and their light-cone counterparts for various flavor-neutral mesons, in the context of the 't Hooft model, that is, the two-dimensional QCD in the large $N$ limit. In contrast to the original derivation via diagrammatic techniques exemplified by Dyson-Schwinger and Bethe-Salpeter equations, here we employ the Hamiltonian operator approach to reconstruct the celebrated 't Hooft equation in light-front quantization, and Bars-Green equations in equal-time quantization. The novelty of our derivation is to employ the soft momentum cutoff as the IR regulator. As a virtue of this operator approach, the functional form of the quasi distributions can be transparently built out of the Bars-Green wave functions and the Bogoliubov angle with the aid of bosonization technique. Equipped with various bound-state wave functions numerically inferred in [1], we then investigate how rapidly the quasi distributions approach their light-cone counterparts with the increasing meson momentum. We observe that, light mesons' quasi distributions approach the light-cone distributions in a slower pace than the heavy quarkonia. Curiously, lattice simulations of quasi distributions in four-dimensional QCD also discover this feature. Furthermore, we also compute the partonic light-cone PDF and quasi-PDF to one-loop order in perturbation theory, again employing the momentum cutoff as the IR regulator. We explicitly verify one of the backbones underlying the large momentum effective field theory (LaMET), namely, both quasi-PDFs and light-cone PDFs in ${\rm QCD}_2$ indeed possess the same IR behavior at leading order in $1/P^z$