Multiparticle Veneziano Formulas Corresponding to Minimal Nonplanar Feynman Diagrams

A new class of multiparticle Veneziano formulas is constructed. The amplitudes correspond to a subclass of nonplanar Feynman diagrams without internal vertices which we call minimal diagrams, just as the current multiparticle Veneziano formulas correspond to planar diagrams. For simplicity, we have not examined diagrams with more than one crossed line. The r-point function is represented by an (r-3)-dimensional integral, as it is for planar diagrams. While the new formula has many properties in common with the old one, the three-particle channels of the Feynman diagram have a more complicated spectrum which suggests a system of three quarks.