On the massless tree-level S-matrix in 2d sigma models

Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d [ image ]-models expanded near the trivial vacuum. We find that, in contrast to the standard massive case, there is no apparent link between massless S-matrices and integrability: in well-known integrable models the tree-level massless S-matrix fails to factorize and exhibits particle production. Such tree-level particle production is found in several classically integrable models: the principal chiral model, its classically equivalent 'pseudo-dual' model, its non-abelian dual model and also the [ image ] coset model. The connection to integrability may, in principle, be restored if one expands near a non-trivial vacuum with massive excitations. We discuss IR ambiguities in 2d massless tree-level amplitudes and their resolution using either a small mass parameter or the [ image ]-regularization. In general, these ambiguities can lead to anomalies in the equivalence of the S-matrix under field redefinitions, and may be linked to the observed particle production in integrable models. We also comment on the transformation of massless S-matrices under [ image ]-model T-duality, comparing the standard and the 'doubled' formulations (with T-duality covariance built into the latter).