High-energy status of derivative analyticity relations

Abstract

Asymptotic correlations between the phase delta (E) and the first derivative of the modulus vertical-barF (E) vertical-bar are proved to follow from the general principles of axiomatic quantum field theory (F (E) is the crossing-even or crossing-odd forward scattering amplitude), provided that certain additional assumptions concerning the properties of F (E) at infinite energy are satisfied. Analogous correlations hold, e.g., between ReF (E) and ImF (E). The asymptotic relations obtained resemble the derivative analyticity relations of Bronzan et al.; the main difference is that we introduce only the first derivative, deal with a considerably wider class of functions, and consider exclusively the high-energy asymptotic limit. Some of our relations represent a generalization of Gribov's and Midgal's result, extending its validity from the frame of Regge theory to a general consequence of axiomatic field theory. Problems related to applications are discussed.