Abstract
In this paper we study factorising twists of the massless and integrable R-matrices, and explore the programme of analysis of form factors which Maillet et al developed for ordinary spin-chains. We derive the factorising twists from the universal R-matrix of the Yangian double, and discuss the RTT relations for the two- and three-site monodromy matrix. We show how the twist can be used to compute a simple scalar product. We then implement our construction in the language of free fermions. Finally, we show how to obtain the massless quantum R-matrix from the Yangian universal R-matrix, and compute a peculiar factorising twist for this case as well.