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

$\text{Kbar}N$ 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 $p_K^{lab}\le$ 250 MeV/c. We produce predictions for the $\mathrm{\Sigma }\pi$ mass spectrum, and scattering lenghts $a_{K^{-}p}$, $a_n(K^-n \to K^-n)$,$a_n0(\Kbar0 n \to \Kbar0 n)$,and$a_{ex}(K^-p \to \Kbar0 n)$\mathrm{.}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 $\Kbar N$dataarewellreproducedandourbestresultsforthe$K^-p$and$K^-d$scatteringlenghtsare$a_{K^-p} = (-0.90 + i 0.87) fm$and$A_{K^-d} = (-1.80

• i 1.55) fm$.