What binds quarks together at different momentum scales? A conceptual scenario

TL;DR

This paper explores how quark binding within hadrons varies across momentum scales, using the pion distribution amplitude and concepts from complex systems to connect nonperturbative effects and asymptotic behavior.

Contribution

It introduces a conceptual scenario linking quark binding mechanisms at different scales with synchronization phenomena and analyzes the evolution of the pion distribution amplitude.

Findings

At low scales, quarks are correlated by nonlocal condensates leading to a bimodal distribution.

As momentum increases, evolution effects centralize the distribution, approaching the asymptotic form.

The study connects nonperturbative QCD effects with the asymptotic behavior of the pion distribution amplitude.

Abstract

The binding effects of quarks within hadrons are discussed in terms of the pion distribution amplitude over longitudinal momentum fractions. To understand the behavior of this quantity at different momentum scales, the concept of synchronization in complex systems has been employed. It is argued that at low momentum scales, the quarks get correlated by nonlocal quark/gluon condensates that cause an endpoint-suppressed, mainly bimodal structure of the pion distribution amplitude inferred from a sum-rule analysis. The mass generation mechanism, within the framework of Dyson-Schwinger equations, and evolution effects pull these two peaks back to the center to form at $Q^2\to\infty$ the asymptotic distribution amplitude which represents the most synchronized $\bar{q}q$ state.