Long-Range-Potential Model of Hadrons

A hadron model is proposed in which nonasymptotic quarks interact with a coherent and long-range vector-gluon field, with a resulting linearly rising spectrum. Solutions for $L=0\mathrm{}$ pseudoscalar and vector mesons in this model exhibit an S${\mathrm{U}}_6$-type structure. The pion decay constant and the $\rho -\gamma$ coupling constant for the unperturbed ground states satisfy the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation and have the right order of magnitude. The ratio $\frac{\sigma (e^{+}+e^{-}\to \mathrm{vector}\mathrm{mesons})}{\sigma (e^{+}+e^{-}\to {\mu }^{+}+{\mu }^{-})}$ decreases like $s^{\frac{-1\mathrm{}}{2}}$ in the present model, whereas it is shown that the ratio approaches a constant in the three-dimensional oscillator-potential model.