The Hadron-Parton Bridge, From the QCD Vacuum to Partons

TL;DR

The Hadron-Parton Bridge presents a coherent framework that unifies the rest-frame hadron spectroscopy dictated by confinement and chiral symmetry breaking with the high-energy, parton-based picture encoded in PDFs, DAs, GPDs, and related observables. By anchoring light-front Hamiltonians in the nonperturbative QCD vacuum via the Instanton Liquid Model and implementing controlled boosts through gradient-flow regularization, the authors derive realistic nonperturbative inputs for partonic observables at a low matching scale, then connect them to perturbative QCD via gradient-flow renormalization and MS-bar matching followed by DGLAP/ERBL evolution. The approach naturally yields predictions for spoke-and-space: mesons, baryons, tetraquarks, pentaquarks, and higher multiquark states, including their spectra and partonic structures, as well as gravitational form factors and EMT properties. A key theme is the explicit, Wilsonian continuity between confinement-driven hadron structure and parton-level descriptions, enabling a transparent, multiscale description of QCD bound states. The work also engages with lattice-based LaMET comparisons, emphasizes vacuum topology’s role in shaping spectra and distributions, and demonstrates substantial predictive power for both spectroscopy and partonic observables across conventional and exotic hadrons. This unified framework has significant implications for interpreting experimental data (e.g., heavy-quarkonia spectra, tetraquark/pentaquark candidates) and for guiding future nonperturbative computations of PDFs, GPDs, and EMT-related observables from first principles.

Abstract

Quantum Chromodynamics (QCD) exhibits complementary descriptions of hadrons: a rest-frame picture based on confinement, chiral symmetry breaking and interquark forces, and a high-energy light-front picture expressed through parton distributions (PDFs,TMDs,GPDs) and form factors. This review develops a unified framework that connects these two domains. It is based mostly on multiple studies by the authors in the past few years. Using the Instanton Liquid Model (ILM) to capture essential nonperturbative features of the QCD vacuum, we derive effective interactions for mesons, baryons, and multiquark states, construct their wave functions in hyperspherical coordinates, and boost them to the light front. The resulting light-front Hamiltonians, incorporating both perturbative and instanton-induced dynamics in the Wilsonian spirit, provide realistic nonperturbative inputs for computing PDFs, DAs, GPDs, quasi-distributions, and gravitational form factors at a well-defined low scale. The connection to perturbative QCD is then established by matching gradient-flow-renormalized operators and LF wave functions to the standard $\overline{\rm MS}$ scheme. Perturbative DGLAP and ERBL evolution then connects these predictions to experimentally accessible regimes. % This approach is applied to quarkonia, glueballs, light mesons, baryons, tetraquarks, pentaquarks, and higher multiquark hadrons, yielding consistent descriptions of both their spectra and partonic structure. Special emphasis is placed on the energy-momentum tensor and the mechanical properties of hadrons, which emerge naturally from the same dynamical ingredients. Overall, the framework demonstrates a clear continuity between hadronic spectroscopy and partonic observables, offering a coherent multiscale picture of hadron structure rooted in the underlying dynamics of QCD.

Figures (95)

• Figure 2.1.1: The correlator of two local operators with the quantum numbers of the rho-meson (upper, V) and the pion (lower, P), normalized to propagation of free massless quarks. Note that the upper plot is linear and the lower logarithmic, as nonperturbative corrections in the pion channel are much larger. The dotted lines are contributions of the lowest state, the dashed ones those of non-resonance continuum.
• Figure 2.1.2: The left sketch shows a pion propagating through the instanton vacuum; the right shows a nucleon. In the latter, the $ud$ pair forms "good diquarks". Blue dots mark quark mass insertions where chirality flips occur.
• Figure 2.2.1: A sketch illustrating the "bridge" to be discussed.
• Figure 2.5.1: Flavor asymmetry of the antiquark sea as the ratio $\bar{d}/\bar{u}$ versus momentum fraction $x$, from 2103.04024.
• Figure 3.1.1: The splitting of the negative-parity state from the vacuum, $gap=E_- - E_+$, shown as data points. The three curves correspond to one-, two-, and three-loop semiclassical approximations.