Tree-level elastic 2d theories with polynomial interactions remain elastic at one loop once masses are renormalized by bubble diagrams, with a universal one-loop S-matrix in terms of tree-level data.
Singularity analysis in $A_n$ Affine Toda Theories
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abstract
The leading and the subleading Landau singularities in affine Toda field theories are examined in some detail. Formulae describing the subleading simple pole structure of box diagrams are given explicitly. This leads to a new and nontrivial test of the conjectured exact S-matrices for these theories. We show that to the one-loop level the conjectured S-matrices of the $A_n$ Toda family reproduce the correct singularity structure, leading as well as subleading, of the field theoretical amplitudes. The present test has the merit of being independent of the details of the renormalisations.
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One-loop integrability with shifting masses
Tree-level elastic 2d theories with polynomial interactions remain elastic at one loop once masses are renormalized by bubble diagrams, with a universal one-loop S-matrix in terms of tree-level data.