Chiral dynamics of $\Sigma$-hyperons in the nuclear medium

Abstract

Using SU(3) chiral perturbation theory we calculate the density-dependent complex mean field $U_{\Sigma }(k_f)+i{W}_{\Sigma }(k_f)$ of a $\Sigma$-hyperon in isospin-symmetric nuclear matter. The leading long-range $\Sigma N$-interaction arises from one-kaon exchange and from two-pion exchange with a $\Sigma$- or a $\Lambda$-hyperon in the intermediate state. We find from the $\Sigma N\to \Lambda N$ conversion process at nuclear matter saturation density ${\rho }_0=0.16$fm${}^{-3}$ an imaginary single-particle potential of $W_{\Sigma }(k_{f0})=-21.5$ MeV, in fair agreement with existing empirical determinations. The genuine long-range contributions from iterated (second order) one-pion exchange with an intermediate $\Sigma$- or $\Lambda$-hyperon sum up to a moderately repulsive real single-particle potential of $U_{\Sigma }(k_{f0})=59$ MeV. Recently measured $({\pi }^{-},K^{+}$) inclusive spectra related to ${\Sigma }^{-}$-formation in heavy nuclei give evidence for a $\Sigma$-nucleus repulsion of similar size. Our results suggest that the net effect of the short-range $\Sigma N$-interaction on the $\Sigma$-nuclear mean field could be small.

Comments: 7 pages, 2 figures, published in: Phys. Rev. C 71, 068201 (2005)