A Euclidean bridge to the relativistic constituent quark model

Abstract

$\mathbf{Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). $\mathbf{Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. $\mathbf{Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. $\mathbf{Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero. $\mathbf{Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements. The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.

27 pages, 5 figures

References in corpus (8)

• Nucleon Electromagnetic Form Factors
• Nucleon electromagnetic form factors
• Interplay of Spin and Orbital Angular Momentum in the Proton
• Flavour symmetry breaking and meson masses
• Resolution of the Proton Spin Problem
• Determination of polarized parton distribution functions with recent data on polarization asymmetries
• Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
• Constraining nucleon strangeness

Cited by in corpus (4)

• Comparison of two Minkowski-space approaches to heavy quarkonia
• A Bayesian analysis of light-front models and the nucleon's charmed sigma term
• Dressed Quark Tensor Vertex and Nucleon Tensor Charge
• Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach