Bound States and Regge Trajectories in a Vector Meson Exchange Model. I. Application to theKK¯System

Partial-wave dispersion relations, extended to noninteger angular momenta are utilized, together with assumptions on the dominance of one-meson exchange to compute the properties of bound states. The exchanged mesons are represented by Regge poles, which lead to a set of equations of generalized Fredholm type when the $\frac{N}{D}$ technique is applied. Bound-state energies in a one-channel system of two spinless particles are computed, as well as the slope of the Regge trajectory which passes through each bound state; the latter is accomplished by an extension of the $\frac{N}{D}$ formalism to angular momenta in the neighborhood of the positive integers. Threshold questions are treated by an approximation for more complex diagrams. The integral equations are solved without further approximations by electronic computer methods. The model is applied to the $\varphi$ meson as a nearly bound state of the $K\overline{K}$ system in the present work and yields information on $S$-wave $K\overline{K}$ interactions. Application to future "bootstrap" calculations, the reason for computing the Regge slopes, is discussed, as well as the relationship to the strip approximation.