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

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 → ∞ the asymptotic distribution amplitude which represents the most synchronized qq state.

Chimera distribution amplitudes for the pion and the longitudinally polarized ρ -meson

“…Note that the moments ξ N π coincide by construction with the central moments 2 at the edge of the NLC regime. The solid lines within both regions denote, respectively, the BMS model from [6] and the pk DA discussed in the text and in [4,5]. The broken lines show the unimodal DSE-DB DA (dashed), the DSE-RL DA (dashed-dotted) (both from [9]), and the asymptotic DA (dashed-dotted-dotted).…”

“…The other symbols in both panels denote the following DAs: ★ -bimodal ρ DA from NLC-QCD sum rules [8]; -bimodal ρ DA from NLC-QCD sum rules [18]; ✪ -platykurtic ρ DA (this work); ▼ -ρ DA from lightfront model [39]: • -ρ DA from instanton model [40]; ■ -ρ DA from QCD sum rules [41]; -ρ DA from AdS/QCD [42] △ -π AdS/QCD [43]; ♦ ♦ ♦ -ρ DSE DA [10]; ◆ -asymptotic DA; ✖ (both panels) -BMS π DA [6]; ✜ (both panels) -platykurtic π DA; [4]; ▲ (both panels) -DSE-DB π DA [9]; ▽ (both panels) -DSE-RL π DA [9]. The slanted rectangles, bounded by dashed lines, in both panels display the regions determined in this work for the π DA using NLC QCD sum rules with λ 2 q = 0.45 GeV 2 .…”

“…In particular the pion, the lightest bound state within Quantum Chromodynamics (QCD), provides a suitable "laboratory" for testing new ideas and techniques to catch the main ingredients of the underlying quark-gluon dynamics entering exclusive QCD processes (see [1][2][3] for reviews). In this paper we will present an amplification of the recent analysis by one of us in [4], continued in [5], for the pion and consider its extension to the longitudinally polarized ρ meson (ρ ). The new mode of thought in [4] is based on the ubiquitous phenomenon of synchronization (Sync for short) in complex systems and we will expand the status of this subject towards a deeper understanding of the meson DAs.…”

“…In this paper we will present an amplification of the recent analysis by one of us in [4], continued in [5], for the pion and consider its extension to the longitudinally polarized ρ meson (ρ ). The new mode of thought in [4] is based on the ubiquitous phenomenon of synchronization (Sync for short) in complex systems and we will expand the status of this subject towards a deeper understanding of the meson DAs. In this way, we will redetermine the ρ DA using QCD sum rules with nonlocal condensates (NLC) within the approach developed in [6][7][8].…”

“…Our primary findings to be discussed later can be summarized as follows: First, we provide more details about the structure of the Sync-inspired shorttailed (i.e., endpoint-suppressed) platykurtic (pk) π DA, proposed in [4], and quantify the uncertainties of its expansion coefficients. This DA is a kind of chimera 1 state because it mimics within the NLC-based approach characteristics pertaining to the dynamical chiral symmetry breaking (DCSB) described in terms of Dyson-Schwinger equations (DSE) [9,10].…”