Planar bootstrap based on a Padé approximation to the dual multiperipheral model

We introduce a Padé approximation to the multiperipheral integral equation which becomes exact for a factorizable model, but is much easier to set up, even without simplifying kinematic approximations. We then apply this to a dual multiperipheral model in which the produced clusters are dual to Regge behavior. If we only consider uncrossed loops (in the usual quark-duality sense), the requirement that the resulting output Reggeon be consistent with the input leads to two bootstrap conditions, one of which is similar to the planar bootstrap of Veneziano, but incorporates certain threshold phenomena. If we make the dual-tree approximation for the triple-Regge vertex $g(t^{\prime },t^{\prime \prime },t)$ we obtain a Reggeon intercept ${\alpha }_0\simeq 0.53$ and a value for $g(0,0,0)\mathrm{}$ which is in reasonably good agreement with experiment. The Pomeron can be calculated by adding in crossed (cylinder) loops and again leads to a result which is in reasonable agreement with the data at moderate energies.