$\Sigma$-nuclear spin-orbit coupling from two-pion exchange

TL;DR

This paper calculates the density-dependent spin-orbit coupling of a Sigma hyperon in nuclear matter using chiral perturbation theory, revealing a significant long-range 'wrong-sign' component and the impact of conversion processes.

Contribution

It provides the first calculation of the Sigma hyperon's spin-orbit coupling from long-range pion exchange within chiral perturbation theory, including complex and density-dependent effects.

Findings

Long-range pion exchange induces a sizeable negative spin-orbit coupling.

Conversion processes contribute an imaginary part to the coupling.

Total Sigma-nuclear spin-orbit coupling is weak when short-range effects are included.

Abstract

Using SU(3) chiral perturbation theory we calculate the density-dependent complex-valued spin-orbit coupling strength $U_{\Sigma ls}(k_f)+ i W_{\Sigma ls}(k_f)$ of a $\Sigma$ hyperon in the nuclear medium. The leading long-range $\Sigma N$ interaction arises from iterated one-pion exchange with a $\Lambda$ or a $\Sigma$ hyperon in the intermediate state. We find from this unique long-range dynamics a sizeable ``wrong-sign'' spin-orbit coupling strength of $U_{\Sigma ls}(k_{f0}) \simeq -20$ MeVfm$^2$ at normal nuclear matter density $\rho_0 = 0.16 $fm$^{-3}$. The strong $\Sigma N\to \Lambda N$ conversion process contributes at the same time an imaginary part of $W_{\Sigma ls}(k_{f0}) \simeq -12$ MeVfm$^2$. When combined with estimates of the short-range contribution the total $\Sigma$-nuclear spin-orbit coupling becomes rather weak.