A new perspective on the Faddeev equations and the $\bar{K}NN$ system from chiral dynamics and unitarity in coupled channels

Abstract

We review recent work concerning the $\bar{K}N$ interaction and Faddeev equations with chiral dynamics which allow us to look at the $\bar{K}NN$ 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 $\Lambda (1405)$ 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 the $\bar{K}NN$ 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 of $\bar{K}$-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.

18 pages, 7 figures, one misprint corrected, Nuclear Physics A in press

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Cited by in corpus (17)

• Realistic calculations of Kbar-N-N, Kbar-N-N-N, and Kbar-Kbar-N-N quasibound states
• Novel Six-Quark Hidden-Color Dibaryon States in QCD
• K${}^{-}$ absorption on two nucleons and ppK${}^{-}$ bound state search in the ${\Sigma }^0$p final state
• A narrow $DNN$ quasi-bound state
• $\bar{K}NN$ Absorption within the Framework of the Fixed Center Approximation to Faddeev equations
• Improved Fixed Center Approximation of the Faddeev equations for the $\bar{K}NN$ system with S=0
• A Bohr-type model with gravity as the attractive force
• Faddeev-Chiral Unitary Approach to the $K^{-}d$ scattering length
• A study of $\eta K\bar{K}$ and ${\eta }^{\prime }K\bar{K}$ with the fixed center approximation to Faddeev equations
• Tri-meson bound state $BB{B}^{\ast }$ via delocalized $\pi$~Bond
• Recent developments in antikaon-nucleon dynamics
• Does the Multiple-scattering Series in the Pion-deuteron Scattering Actually Converge?
• Kaon-deuteron femtoscopy from unitarized chiral interactions
• Binding of antikaons and Lambda(1405) clusters in light kaonic nuclei
• Antikaon-nucleon dynamics and its application to few-body systems
• Search for Deeply Bound Kaonic Nuclear States with AMADEUS
• Narrow bound states of the DNN system