We have performed a calculation of the scattering amplitude for the three body systemKN N assuminḡ K scattering against a N N cluster, using the Fixed Center approximation to the Faddeev equations. Thē KN amplitudes, which we take from chiral unitary dynamics, govern the reaction and we find aKN N amplitude that peaks around 40 MeV below theKN N threshold, with a width in |T | 2 of the order of 50MeV for spin 0 and has another peak around 27 MeV with similar width for spin 1. The results are in line with those obtained using different methods but implementing chiral dynamics. The simplicity of the approach allows one to see the important ingredients responsible for the results. In particular we show the effects from the reduction of the size of the N N cluster due to the interaction with theK and those from the explicit considiration of the πΣN channel in the three body equations.

In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly used, is also obtained in Quantum Mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also provides an insight and practical rules for evaluating couplings of the resonances to external sources and how to deal with final state interaction in production processes. As an application of the formalism we evaluate the wave functions of the two Λ(1405) states in the πΣ,KN and other coupled channels. It also offers a practical way to study three body systems when two of them cluster into a resonance.

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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.