A new perspective on the Faddeev equations and the image system from chiral dynamics and unitarity in coupled channels

We review recent work concerning the image interaction and Faddeev equations with chiral dynamics which allow us to look at the image from a different perspective and pay attention to problems that have been posed in previous studies on the subject. We then show results which provide extra experimental evidence on the existence of two image states. Then show the findings of a recent approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two-body off-shell amplitude with three-body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off-shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on-shell two-body amplitudes need to be used. With this information in mind we use an approximation to the Faddeev equations within the fixed center approximation to study the image system, providing answers within this approximation to questions that have been brought before and evaluating binding energies and widths of this three-body system. As a novelty with respect to recent work on the topic we find a bound state of the system with spin image, like a bound state of image-deuteron, less bound that the one of image, where all recent efforts have been devoted. The width is relatively large in this case, suggesting problems in a possible experimental observation.