  In contradistinction to the case of massive excitations, the connection
between integrability and the tree-level massless scattering matrix of
integrable $\sigma$-models is lost. Namely, in well-known 2-d integrable models
the tree-level massless S-matrix exhibits particle production and fails to
factorise. This is conjectured to happen due to IR ambiguities in the massless
tree-level amplitudes. We present a definition of the massless S-matrix which
has all the nice properties of integrable theories, there is no particle
production and the S-matrix factorises. As an example, we present in detail the
case of the $SU(2)$ principal chiral model (PCM).
