Particle Exchange, Regge-Pole Exchange and the Veneziano Amplitude for KN Scattering

Based on the observation that the (t, u)-Veneziano terms can be expressed as an infinite sum of one-particle exchange contributions in the physical region, contrary to the (s, t) and (s, u) terms where the particle exchange picture is divergent, the validity of the particle exchange picture and the transcendental mechanism to the Regge pole exchange picture is examined in a KN Veneziano amplitude consisting of (t, u) terms only. At threshold, the contribution of meson exchanges with the lowest mass almost saturates the KN Veneziano amplitude. The hyperon exchange contributions should be discarded there, because of the duality between meson exchange contributions and hyperon exchange contributions. As energy increases, the meson towers with various spin states and degenerate mass begin to contribute one by one. Regge behaviour is obtained as a result of a detailed cancellation among the contributions of meson exchanges with various masses and spins. Here, Regge behaviour in a limited energy region is given by a finite sum of one-meson exchange terms. On the other hand, the hyperon exchange picture with finite terms does not approximate well the amplitude in the low energy region, even at threshold. These situations are understood through the study of the condition for an approximate truncation of infinite series of poles in the (t, u)-terms. The low energy interpolations of Regge asymptotic forms are studied, and the meson Regge pole exchange is also confirmed to give the gross features of the amplitude down to the threshold. The problem of double counting between the t- and u-Regge poles in low energy is noted