Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics

TL;DR

This paper develops a relativistic energy density functional based on in-medium chiral SU(3) dynamics to accurately describe $ ext{Lambda}$ hypernuclei spectra, explaining the small spin-orbit interaction and matching experimental data.

Contribution

It extends in-medium chiral SU(3) effective field theory to hypernuclei, incorporating density-dependent mean fields and long-range interactions for precise spectral predictions.

Findings

Achieves very good agreement with hypernuclear spectroscopic data.

Explains the small $ ext{Lambda}$-nuclear spin-orbit interaction naturally.

Identifies the role of surface terms consistent with chiral perturbation theory.

Abstract

A previously derived relativistic energy density functional for nuclei, based on low-energy in-medium chiral dynamics, is generalized to implement constraints from chiral SU(3) effective field theory and applied to $\Lambda$ hypernuclei. Density-dependent central and spin-orbit mean fields are calculated for a $\Lambda$ hyperon using the SU(3) extension of in-medium chiral perturbation theory to two-loop order. Long range $\Lambda N$ interactions arise from kaon-exchange and from two-pion-exchange with a $\Sigma$ hyperon in the intermediate state. Short-distance dynamics is encoded in contact interactions. They include scalar and vector mean fields reflecting in-medium changes of quark condensates, constrained by QCD sum rules. The $\Lambda$ single particle orbitals are computed for a series of hypernuclei from $^{13}_{\Lambda}$C to $^{208}_{\Lambda}$Pb. The role of a surface (derivative) term is studied. Its strength is found to be compatible with a corresponding estimate from in-medium chiral perturbation theory. Very good agreement with hypernuclear spectroscopic data is achieved. The smallness of the $\Lambda$-nuclear spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between short-range scalar/vector contributions and longer range terms generated by two-pion exchange.