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

Abstract

We review recent work concerning theKN interaction and Faddeev equations with chiral dynamics which allow us to look at theKN N from a different perspective and pay attention to problems that have been posed in previous studies on the subject. We show results which provide extra experimental evidence on the existence of two Λ(1405) states. We 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 theKN N 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 S=1, like a bound state ofK-deuteron, less bound that the one of S=0, where all recent efforts have been devoted. The width is relatively large in this case, suggesting problems in a possible experimental observation.

K¯NNabsorption within the framework of the fixed-center approximation to Faddeev equations

“…[22] following the steps of [46] for the evaluation of the K − d scattering length. The resulting amplitude is…”

“…However, in more recent papers [19,20], where the energy dependence of the potential is taken from chiral dynamics, the same authors find much smaller binding energies, below 20 MeV. We also calculated theKN N system [21,22] for the S = 0 and S = 1 case, using the Fixed Center Approximation (FCA) to the Faddeev equations taking into account πΣN channel explicitly and also including the charge exchange diagrams. We get a binding of [26][27][28][29][30][31][32][33][34][35] MeV for S = 0 while around 9 MeV for the S = 1 case.…”

Kaonic systems

“…Interestingly, it was also found in [21,22] that a state with J = 1, like a K − d bound state, also appears, with smaller binding but also large width. This state is also found in a more recent work using Faddeev calculations [19], with smaller binding than the one of J = 0.…”

“…Alternative studies to the variational calculations of [17] or the Faddeev calculations of [18,19] are done in [21][22][23] using the fixed center approximation to the Faddeev equations (FCA). One obtains a binding of about 30 MeV and a width of about 50 MeV, which turns out to be 80 MeV when the absorption by two nucleons is included.…”

Does the Multiple-Scattering Series in the Pion–Deuteron Scattering Actually Converge?

“…The FCA is widely used for the K − d scattering problem, see, e.g., [9]. For more recent publications see [10] and references therein.…”