Chiral SU(3) dynamics and Λ hyperons in the nuclear medium -: art. no. 015203

We present a novel approach to the density-dependent mean field and the spin-orbit interaction of a Lambda hyperon in a nuclear many-body system, based on flavor-SU(3) in-medium chiral perturbation theory. The leading long-range LambdaN interaction arises from kaon exchange and from two-pion exchange with a Sigma hyperon in the intermediate state. The empirical Lambda-nucleus potential depth of about -28 MeV is well reproduced with a single cutoff scale, (Lambda) over bar =0.7 GeV, effectively representing all short-distance (high-momentum) dynamics not resolved at scales characteristic of the nuclear Fermi momentum. This value of (Lambda) over bar is remarkably consistent with the one required to reproduce the empirical saturation point of isospin-symmetric nuclear matter in the same framework. The smallness of the Lambda-nuclear spin-orbit interaction finds a natural (yet novel) explanation in terms of an almost complete cancellation between short-range contributions (properly rescaled from the known nucleonic spin-orbit coupling strength) and long-range terms generated by iterated one pion exchange with intermediate Sigma hyperons. The small SigmaLambda-mass difference figures prominently in this context.