Gauge-invariant decomposition of meson energy in two-dimensional QCD

TL;DR

This paper investigates gauge-invariant energy decomposition in a two-dimensional QCD model, revealing new insights into meson energy partitioning and pion behavior, which may inform understanding of real-world QCD.

Contribution

It introduces a gauge-invariant energy decomposition framework in the 't Hooft model, providing novel insights into meson energy distribution and pion properties in two-dimensional QCD.

Findings

Identified patterns in meson energy partitioning across different species.

Discovered unexpected behaviors related to pions in the model.

Provided a basis for future QCD energy decomposition studies.

Abstract

This work is driven by our curiosity towards some basic questions in QCD: how is the energy of a moving hadron partitioned among different gauge-invariant sectors in QCD Hamiltonian? How is the energy of an massless pion separated between quark and gluon sectors, particularly in the soft pion limit? Is it possible to decompose the celebrated Gell-Mann-Oakes-Renner (GOR) relation? To what extent can we justify the quark potential model from the field-theoretical mass decomposition for heavy quarkonium? Due to limitation of contemporary nonperturbative tools, we do not yet know answers to these questions in realistic QCD. In this work, we take the 't Hooft model (two-dimensional QCD in large-$N$ limit) as a prototype model that mimics some essential aspects of the true QCD. We investigate the gauge-invariant energy decomposition of a flavor-neutral meson that can carry an arbitrary momentum (including stationary case), with meson species ranging from massless pion to bottomonium. All the aforementioned questions can be addressed satisfactorily within this model, in particular some unexpected patterns related to pion are discovered for the first time in two-dimensional QCD. We hope that our study can offer some useful clues and stimulation for future investigations on hadron energy decomposition in realistic QCD.