A Classical Interpretation of the Nonrelativistic Quark Potential Model: Color Charge Definition and the Meson Mass-Radius Relationship

Abstract: Quantum Chromodynamics (QCD) is the fundamental theory describing quark interactions, and various quark models based on QCD have been widely used to study the properties of hadrons, including their structures and mass spectra. However, unlike Quantum Electrodynamics (QED) and the Bohr model of the hydrogen atom, there is no direct classical analogy for hadronic structures.This paper presents a classical interpretation of the nonrelativistic quark potential model, providing a more intuitive and visualizable description of strong interactions through the quantitative formulation of color charge and color flux.Furthermore, we establish the relationship between meson mass and its structural radius in the nonrelativistic framework and estimate the key parameters of our model using available data from $\eta_b(1S)$ and $\Upsilon(1S)$. We then extend this relationship to a broader range of excited meson states, obtaining structural radii that show good agreement with the root mean square (RMS) radius or charge radius predicted by QCD calculations.