Dynamical Model of Hadrons with Fermion Quarks

Abstract

A dynamical quark model of hadrons is constructed in terms of the usual triplet of fractionally charged spin-½ quarks ($q$). They have a light mass ($\approx 300$ MeV) and obey Fermi-Dirac statistics. In approximate nonrelativistic terms, the quark interactions are assumed to be described by a long-range effective single-particle Hartree potential with infinitely rising walls and by a strong short-range Yukawa-type one between quark pairs. These combine to prevent single-quark emission from a hadron and to give the observed early scaling and the asymptotic electromagnetic form factors $\sim \frac{1}{t^2}$. The energy-momentum propagating in the field between the interacting quarks is idealized as a virtual particle (the "core" of the baryon) so that the center of mass of the three quarks in the baryon and of the $q\overline{q}$ in the meson is not constrained. Implications of this model are discussed—in particular, the baryon wave functions and energy spectrum, the form-factor behavior, the Adler anomaly for ${\pi }^0\to 2\gamma$ decay, and the hadronic interactions.