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

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