Bootstrap Calculation of theK*Meson Using the Effective-Potential Method

Abstract

We use the effective-potential method of Bal\'azs, with tensor-meson as well as vectormeson exchange included as suggested by an earlier calculation in the $\ensuremath{\pi}\ensuremath{\pi}$ case, to calculate $\ensuremath{\pi}K$ scattering. Taking the strengths of the potentials due to the exchange of other particles from the experimental parameters of the particles, we "bootstrap" the ${K}^{*}$, and obtain self-consistent values for the ${K}^{*}$ mass and width of 930 MeV and 50 MeV, in very good agreement with experiment. Some uncertainty in the predicted values, especially of the mass, results from the necessity of using SU(3) to obtain the $\ensuremath{\rho}K\overline{K}$ coupling, and the fact that the experimental values of the $\ensuremath{\rho}$ and ${K}^{*}$ widths suggest substantial SU(3) breaking. Results for other partial waves of the $\ensuremath{\pi}K$ system are presented, and output ${K}^{*}$ and ${K}^{**}$ Regge trajectories, with slopes about \textonehalf{} and $\frac{1}{3}$ of the "canonical" value of 1 Be${\mathrm{V}}^{\ensuremath{-}2}$, respectively, are obtained.