Planar bootstrap without the dual-tree approximation

Abstract

We consider a dual multiperipheral model at and near $t=0$, and argue that the usual imposition of a Regge-cluster finite-energy sum rule is probably redundant. Instead we require that the $\ensuremath{\pi}\ensuremath{\pi}$ amplitude satisfy the Adler PCAC (partial conservation of axial-vector current) condition and crossing near $s=t=0$. We then set up a specific Pad\'e approximation to the multiperipheral model. This becomes exact for a factorizable model, but takes into account transverse-momentum effects and explicitly incorporates the deferred thresholds arising from the production of clusters. We do not make the dual-tree approximation for our Reggeon couplings, which we represent instead by a more general exponential form. If we then assume a linear Reggeon trajectory $\ensuremath{\alpha}(t)$, self-consistency gives an intercept $\ensuremath{\alpha}(0)=0.49$ and a triple-Regge coupling which is in reasonable agreement with experiment. There are no arbitrary parameters in our model.