Low energy Kbar N interactions and Faddeev calculation of the K- d scattering length in isospin and particle bases

$Kbar N$ interactions are investigated {it via} an effective non-linear chiral meson-baryon Lagrangian. The adjustable parameters are determined by a fitting procedure on the $K^-p$ threshold branching ratios and total cross-section data for $p^{lab}_Kle$ 250 MeV/c. We produce predictions for the $Sigma pi$ mass spectrum, and scattering lenghts $a_{K^-p}$, $a_n(K^-n to K^-n)$, $a_n0(Kbar0 n to Kbar0 n)$, and $a_{ex}(K^-p to Kbar0 n)$. The $Kbar N$ amplitudes thus obtained, as well as those for other two-body channels ($pi N$, $NN$, and $YN$) are used as input to predict the scattering length $A_{K^-d}$, for which we have devised a relativistic version of the three-body Faddeev equations. Results for all two- and three-body coupled channels are reported both in isospin and particle bases. All available $Kbar N$ data are well reproduced and our best results for the $K^-p$ and $K^-d$ scattering lenghts are $a_{K^-p} = (-0.90 + i 0.87) fm$ and $A_{K^-d} = (-1.80 + i 1.55) fm$.