Asymptotic planarity: An S-matrix basis for the Okubo-Zweig-Iizuka rule

A mechanism is exhibited that monotonically depresses the cylinder component of the topological expansion with increasing t, and it is conjectured that all non-planar S-matrix components diminish as t increases, exchange degeneracy and the Okubo-Zweig-Iizuka rule becoming more accurately satisfied. Such asymptotic planarity is compared to the field-theoretical concept of asymptotic freedom. The characteristics low-t cylinder "quenching interval" is found to be the inverse of the mean value over a two-reggeon loop, of 1 2π²(α′)²(t₁ - t₂)²/(-t), where t₁ and t₂ are the squared masses of the loop reggeons and α′ is the trajectory slope. For leading trajectories the low-t cylinder quenching interval is predicted by this formula to be roughly 0.5 GeV²-consistent with the observed pomeron intercept and slope, with the p-ω and f-A₂ mass differences and with the (φ,ω) deviation from ideal mixing. As t grows negatively over a corresponding interval, it is predicted that the pomeron will become nearly a pure SU(3) singlet. If the pion mass helps to set the scale for reggeon loops coupled to unnatural-parity trajectories, the cylinder quenching interval will be larger, explaining the large (η, η′) deviation from ideal mixing as well as the large π-η mass difference. Even when the small-t cylinder quenching is rapid ("precocious planarity") the large-t approach to the planar limit turns out to be gentle. A by-product of this study is an explanation of the approximate reality and linearity of trajectories at large t.