Hypernuclei and in-medium chiral dynamics

TL;DR

This paper extends a relativistic nuclear energy density functional to hypernuclei, using in-medium chiral dynamics to explain the small spin-orbit splitting of the $Lambda$ hyperon through a balance of long-range and short-range interactions.

Contribution

It introduces a novel approach combining in-medium chiral perturbation theory with density functionals to describe hypernuclear structure, especially the $Lambda$ hyperon.

Findings

The model explains the small $Lambda$ spin-orbit potential naturally.

Long-range kaon and two-pion exchange interactions are key.

Scalar and vector mean fields produce significant short-range effects.

Abstract

A recently introduced relativistic nuclear energy density functional, constrained by features of low-energy QCD, is extended to describe the structure of hypernuclei. The density-dependent mean field and the spin-orbit potential of a $\Lambda$-hyperon in a nucleus, are consistently calculated using the SU(3) extension of in-medium chiral perturbation theory. The leading long-range $\Lambda N$ interaction arises from kaon-exchange and $2\pi$-exchange with a $\Sigma$-hyperon in the intermediate state. Scalar and vector mean fields, originating from in-medium changes of the quark condensates, produce a sizeable {\em short-range} spin-orbit interaction. The model, when applied to oxygen as a test case, provides a natural explanation for the smallness of the effective $\Lambda$ spin-orbit potential: an almost complete cancellation between the background contributions (scalar and vector) and the long-range terms generated by two-pion exchange.