Σ-nuclear spin-orbit coupling from two-pion exchange

Using SU(3) chiral perturbation theory we calculate the density-dependent complex-valued spin-orbit coupling strength UΣls(kf)+iWΣls(kf) of a Σ hyperon in the nuclear medium. The leading long-range ΣN interaction arises from iterated one-pion exchange with a Λ or a Σ hyperon in the intermediate state. We find from this unique long-range dynamics a sizable "wrong-sign" spin-orbit coupling strength of UΣls(kf0)-20 MeV fm2 at normal nuclear matter density ρ0=0.16 fm-3. The strong ΣN→ΛN conversion process contributes at the same time an imaginary part of WΣls(kf0)-12 MeV fm2. When combined with estimates of the short-range contribution the total Σ-nuclear spin-orbit coupling becomes rather weak.