In-medium $\Lambda$ isospin impurity from charge symmetry breaking in the ${_{\Lambda}^4}{\rm H}-{_{\Lambda}^4}{\rm He}$ mirror hypernuclei

TL;DR

This paper investigates charge symmetry breaking in mirror hypernuclei, revealing a significant in-medium isospin impurity in the $ extLambda$ hyperon, consistent with historical and lattice QCD results, and explores its effects on $ extLambda$-nucleon interactions.

Contribution

The study quantifies the in-medium $ extLambda - extSigma^0$ admixture and links it to charge symmetry breaking effects in hypernuclei using effective field theory and flavor symmetry considerations.

Findings

In-medium $ extLambda - extSigma^0$ admixture amplitude is about 1.5%.

Results confirm the free-space admixture value from historical and lattice studies.

Charge symmetry breaking impacts $ extLambda$-nucleon spin channels differently, with the $S=0$ channel dominating.

Abstract

The $\Lambda$ separation energies in the mirror hypernuclei ${_{\Lambda}^4}{\rm H}-{_{\Lambda}^4}{\rm He}$ exhibit large charge symmetry breaking (CSB). Analyzing this CSB within pionless effective field theory while using partially conserved baryon-baryon SU(3) flavor symmetry, we deduce a $\Lambda -\Sigma^0$ induced in-medium admixture amplitude ${\cal A}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0$ $\Lambda$ hyperon. Our results confirm the free-space value ${\cal A}^{(0)}_{I=1}$ inferred directly within the SU(3) baryon octet by Dalitz and von-Hippel in 1964 and reaffirmed in a recent QCD+QED lattice calculation. Furthermore, exploring the consequences of SU(3) flavor symmetry on the $\Lambda$-nucleon interaction, we find that CSB is expected to impact the $S=1$ and $S=0$ spin channels in opposite directions, with the latter dominating by an order of magnitude. These observations explain a recent deduction of $\Lambda$-nucleon CSB strengths.