Bound state scattering simplified

In the description of the AdS(5)/CFT4 duality by an integrable system the scattering matrix for bound states plays a crucial role: it was initially constructed for the evaluation of finite size corrections to the planar spectrum of energy levels/anomalous dimensions by the thermodynamic Bethe ansatz, and more recently it reappeared in the context of the gluing prescription of the hexagon approach to higher-point functions. In this work we present a simplified form of this scattering matrix and we make its pole structure manifest. We find some new relations between its matrix elements and also present an explicit form for its inverse. We finally discuss some of its properties including crossing symmetry. Our results will hopefully be useful for computing fmite-size effects, in particular for simplifying the complicated sum integrals arising from the gluing of hexagons, as well as help towards understanding universal features of the AdS(5)/CFT4 scattering matrix.