Low energyK¯Ninteractions and Faddeev calculation of theK−dscattering length in isospin and particle bases

Abstract

$\overline{K}N$ interactions are investigated via an effective nonlinear chiral meson-baryon Lagrangian. The adjustable parameters are determined by a fitting procedure on the ${K}^{\ensuremath{-}}p$ threshold branching ratios and total cross-section data for ${p}_{K}^{lab}\ensuremath{\leqslant}250\phantom{\rule{0.3em}{0ex}}\text{MeV}∕c$. We produce predictions for the $\ensuremath{\Sigma}\ensuremath{\pi}$ mass spectrum, and scattering lengths ${a}_{{K}^{\ensuremath{-}}p}$, ${a}_{n}({K}^{\ensuremath{-}}n\ensuremath{\rightarrow}{K}^{\ensuremath{-}}n)$, ${a}_{n}^{\ensuremath{\circ}}({\overline{K}}^{\ensuremath{\circ}}n\ensuremath{\rightarrow}{\overline{K}}^{\ensuremath{\circ}}n)$, and ${a}_{ex}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{\ensuremath{\circ}}n)$. The $\overline{K}N$ amplitudes thus obtained, as well as those for other two-body channels ($\ensuremath{\pi}N$, $NN$, and $YN$), are used as input to predict the scattering length ${A}_{{K}^{\ensuremath{-}}d}$, 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 $\overline{K}N$ data are well reproduced and our best results for the ${K}^{\ensuremath{-}}p$ and ${K}^{\ensuremath{-}}d$ scattering lengths are ${a}_{{K}^{\ensuremath{-}}p}=(\ensuremath{-}0.90+i0.87)$ fm and ${A}_{{K}^{\ensuremath{-}}d}=(\ensuremath{-}1.80+i1.55)$ fm.