Locality and Analyticity of the Crossing Symmetric Dispersion Relation

TL;DR

This paper explores the locality and analyticity properties of the crossing symmetric dispersion relation, introducing a new expansion called Feynman block expansion with improved convergence and analyticity features.

Contribution

It introduces the Feynman block expansion for crossing symmetric dispersion relations, providing a formula for contact terms and analyzing its analyticity domain.

Findings

Feynman block expansion is fully crossing symmetric and local.

The analyticity domain of the expansion is larger than traditional methods.

Super-string amplitude examples show better convergence of the expansion.

Abstract

This paper discusses the locality and analyticity of the crossing symmetric dispersion relation (CSDR). Imposing locality constraints on the CSDR gives rise to a local and fully crossing symmetric expansion of scattering amplitudes, dubbed as Feynman block expansion. A general formula is provided for the contact terms that emerge from the expansion. The analyticity domain of the expansion is also derived analogously to the Lehmann-Martin ellipse. Our observation of type-II super-string tree amplitude suggests that the Feynman block expansion has a bigger analyticity domain and better convergence.