Why the constituent interchange model does not predict the dimensional counting rule to any finite order in QCD

Abstract

We demonstrate that the constitutent interchange diagram for nucleon nucleon elastic scattering contains a pinch singularity. This means that it predicts that\(\frac{{d\sigma }}{{dt}} \sim s^{ - 9} f\left( \theta \right)\) for high energy elastic scattering, at least to any finite order in QCD. We also show how the dimensional counting rule may perhaps be recovered by summing a suitable infinite series of graphs.