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

Abstract

$\text{Kbar}N$ 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 $\Sigma \pi$ mass spectrum, and scattering lenghts $a_{K^{-}p}$, $a_n(K^{-}n\to K^{-}n)$, $a_{n}0(\text{Kbar}0n\to \text{Kbar}0n)$, and $a_{ex}(K^{-}p\to \text{Kbar}0n)$. The $\text{Kbar}N$ 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 $\text{Kbar}N$ data are well reproduced and our best results for the $K^{-}p$ and $K^{-}d$ scattering lenghts are $a_{K^{-}p}=(-0.90+i0.87)fm$ and $A_{K^{-}d}=(-1.80+i1.55)fm$.

Comments: 31 pages, submitted to Phys. Rev. C