Integrable deformations of the O(3) sigma model. The sausage model

We consider two one-parameter families of two-dimensional relativistic factorized scattering theories, which are deformations of the ones characteristic for the two-dimensional O(3) sigma models with θ = 0 and θ = π. The Bethe ansatz technique is applied to these two families to justify their interpretation as the factorized scattering theories of certain O(2)-symmetric deformations of the O(3) sigma model (the sausage model). The result suggests that the sausage model is integrable at the topological angle values θ = 0 or θ = π.