The dual parton picture

Abstract

We make more quantitative the recent speculations that the N -point Veneziano amplitude can be viewed as the limit of very high-order unrenormalized Feynman diagrams. A general statistical formalism for investigating the behaviour of very high-order Feynman diagrams is developed. Within the framework of the electric-circuit analogy the concept of the mean resistance of a propagator is introduced. It is shown that the combined effect of the fluctuations around the mean resistance is smaller than one would expect. It then follows that a family of n -dimensional integrals over Feynman parameters can be evaluated in the limit n → ∞. This implies that the Feynman amplitude with soft (“wee”) virtual particles (partons) can be replaced by a simple Gaussian expression (with no loop integrations) to a good approximation in the limit of very high order, provided the parton Lagrangian contains a super-renormalizable φ 3 part. Having obtained this result, Nielsen's variational principle follows if the discrete Feynman net is replaced by a continuous distribution of propagators. The Regge slope is expressed in terms of the parton mass.