Analytic QCD Binding Potentials

TL;DR

This paper develops analytic forms of non-perturbative QCD binding potentials for mesons and baryons using a gauge-invariant approach, providing insights into their mass contributions and ground state energies.

Contribution

It introduces a novel analytic method to derive QCD binding potentials for quark-antiquark and three-quark systems within a gauge-invariant framework, simplifying complex equations.

Findings

Derived explicit binding potentials for mesons and baryons.

Estimated lowest quark masses and gluon energy contributions.

Identified a new parameter influencing the formalism.

Abstract

This paper applies the analytic forms of a recent non-perturbative, manifestly gauge- and Lorentz-invariant description (of the exchange of all possible virtual gluons between quarks ($Q$) and/or anti-quarks ($\bar{Q}$) in a quenched, eikonal approximation) to extract analytic forms for the binding potentials generating a model $Q$-$\bar{Q}$ "pion", and a model $QQQ$ "nucleon". Other, more complicated $Q$, $\bar{Q}$ contributions to such color-singlet states may also be identified analytically. An elementary minimization technique, relevant to the ground states of such bound systems, is adopted to approximate the solutions to a more proper, but far more complicated Schroedinger/Dirac equation; the existence of possible contributions to the pion and nucleon masses due to spin, angular momentum, and "deformation" degrees of freedom is noted but not pursued. Neglecting electromagnetic and weak interactions, this analysis illustrates how the one new parameter making its appearance in this exact, realistic formalism may be evaluated, along with a qualitative estimate of the lowest quark mass and the energy contributions to the ground states of the gluon fields, from a knowledge of the pion and (ground state) nucleon masses.