Testing for new phenomena in high energy elastic scattering

We discuss and enlarge upon a very neat and succinct relation proposed recently by Giffon, Predazzi and Samokhin, linked to the behaviour of elastic scattering at asymptotically high energies. We demonstrate that their result, which was established within a limited class of possible asymptotic behaviours, is actually extremely general and can be proved in an essentially axiomatic framework. We discuss how this relation can be used as a basis for detecting new phenomena at RHIC and LHC energies.