From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients

TL;DR

This paper analyzes the structure of poles in the S-matrices of affine Toda theories, deriving singularity coefficients using perturbation theory and tree-level diagrams, confirming consistency with known bootstrap results.

Contribution

It provides a universal method to compute Laurent expansion coefficients of S-matrix poles in affine Toda theories using perturbation theory and tree diagrams.

Findings

Derived coefficients of singularities at poles using one-loop perturbation theory.

Established a universal approach independent of specific theories.

Confirmed results align with conjectured bootstrap S-matrices for ADE theories.

Abstract

Various features of the even order poles appearing in the S-matrices of simply-laced affine Toda field theories are analysed in some detail. In particular, the coefficients of first- and second-order singularities appearing in the Laurent expansion of the S-matrix around a general $2N^{\rm th}$ order pole are derived in a universal way using perturbation theory at one loop. We show how to cut loop diagrams contributing to the pole into particular products of tree-level graphs that depend on the on-shell geometry of the loop; in this way, we recover the coefficients of the Laurent expansion around the pole exploiting tree-level integrability properties of the theory. The analysis is independent of the particular simply-laced theory considered, and all the results agree with those obtained in the conjectured bootstrapped S-matrices of the ADE series of theories.