Field-theoretic model of composite hadrons. I

Abstract

We discuss here a field-theoretic model of composite hadrons with quarks. The quark field operators are assumed to be broken up into particle and antiparticle components at any time $t$ similar to the large and small components of a free-Dirac-field operator. This assumption is made consistent with equal-time anticommutators. This implies that the Dirac Hamiltonian for quark field operators has four components: the particle, antiparticle, pair-creation, and pair-annihilation components. For a simple ansatz for the field operators, the latter two components need not vanish. The particle and antiparticle components along with some potential-like interactions are assumed to generate the hadrons as composite states. With the usual form of weak and electromagnetic currents, this yields some corrections to the Van Royen-Weisskopf relations and gives excellent agreement for the static properties of the nucleons. It is seen that the pair-creation component of the Hamiltonian can generate $\phi \to \mathrm{KK}$ decay, with a correct branching ratio for $\frac{\Gamma (\phi \to K^{+}{K}^{-})}{\Gamma (\phi \to K^0{\overline{K}}^0)}$. Thus, the pair-creation Hamiltonian seems to be the dynamical explanation of the Okubo-Zweig-Iizuka rule. Further, the pair-annihilation component of the Hamiltonian with minimal electromagnetic interaction also generates $\Gamma ({\pi }^0\to 2\gamma )$. With the mixing angle obtained from the quadratic mass formula, $\Gamma (\eta \to 2\gamma )$ also seems to have a reasonable prediction. We have considered only nonrelativistic hadrons hoping that a potential-like description is valid in such a frame of reference.