Chiral dynamics of $Σ$-hyperons in the nuclear medium

Abstract

Using SU(3) chiral perturbation theory we calculate the density-dependent complex mean field $U_Σ(k_f)+ i W_Σ(k_f)$ of a $Σ$-hyperon in isospin-symmetric nuclear matter. The leading long-range $ΣN $-interaction arises from one-kaon exchange and from two-pion exchange with a $Σ$- or a $Λ$-hyperon in the intermediate state. We find from the $ΣN\to ΛN$ conversion process at nuclear matter saturation density $ρ_0 = 0.16 $fm$^{-3}$ an imaginary single-particle potential of $W_Σ(k_{f0}) =-21.5$ MeV, in fair agreement with existing empirical determinations. The genuine long-range contributions from iterated (second order) one-pion exchange with an intermediate $Σ$- or $Λ$-hyperon sum up to a moderately repulsive real single-particle potential of $U_Σ(k_{f0})= 59$ MeV. Recently measured $(π^-,K^+$) inclusive spectra related to $Σ^-$-formation in heavy nuclei give evidence for a $Σ$-nucleus repulsion of similar size. Our results suggest that the net effect of the short-range $ΣN$-interaction on the $Σ$-nuclear mean field could be small.