Faddeev-Chiral Unitary Approach to the $K^- d$ scattering length

Our earlier Faddeev three-body study in the $K^-$-deuteron scattering length, $A_{K^-d}$, is revisited here in the light of the recent developments in two fronts: {\it (i)} the improved chiral unitary approach to the theoretical description of the coupled $\Kbar N$ related channels at low energies, and {\it (ii)} the new and improved measurement from SIDDHARTA Collaboration of the strong interaction energy shift and width in the lowest $K^-$-hydrogen atomic level. Those two, in combination, have allowed us to produced a reliable two-body input to the three-body calculation. All available low-energy $K^-p$ observables are well reproduced and predictions for the $\Kbar N$ scattering lengths and amplitudes, $(\pi \Sigma)^\circ$ invariant-mass spectra, as well as for $A_{K^-d}$ are put forward and compared with results from other sources. The findings of the present work are expected to be useful in interpreting the forthcoming data from CLAS, HADES, LEPS and SIDDHARTA Collaborations.