Dynamical Model of theK*Resonance

Abstract

The $K^{*}$ vector meson is regarded as a $P$-wave resonance in the coupled, isotopic spin ½, $\pi +K$, and $\eta +K$ states. All forces other than the $K^{*}$ and $\rho$ exchange forces are neglected, and a modification of the self-consistency technique of Zachariasen and Zemach is used to calculate the $K^{*}$ mass and two relations among the three coupling-constant products ${{\gamma }_{K^{*}\pi K}}^2$, ${{\gamma }_{K^{*}\eta K}}^2$, and ${\gamma }_{\rho \pi \pi }{\gamma }_{\rho \mathrm{KK}}$. The calculated $K^{*}$ mass agrees with experiment. The factors in the self-consistency equations that depend on the $\pi -\eta -K$ and $K^{*}-\rho$ mass differences are isolated, and the effects of these mass differences on the results are discussed. The relationship of the results to the predictions of unitary symmetry is discussed.