The $\mathrm{\Lambda }$ separation energies in the mirror hypernuclei ${}_{\mathrm{\Lambda }}^4\mathrm{H}\text{−}{}_{\mathrm{\Lambda }}^4\mathrm{He}$ 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 $\mathrm{\Lambda }\text{−}{\mathrm{\Sigma }}^0$ induced in-medium admixture amplitude ${\mathcal{A}}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0\mathrm{\Lambda }$ hyperon. Our results confirm the free-space value ${\mathcal{A}}_{I=1}^{\left(0\right)}$ inferred directly within the SU(3) baryon octet by Dalitz and von Hippel in 1964 and reaffirmed in a recent $\mathrm{QCD}+$QED lattice calculation. Furthermore, exploring the consequences of SU(3) flavor symmetry on the $\mathrm{\Lambda }$-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 $\mathrm{\Lambda }$-nucleon CSB strengths.

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• Few-body systems
• Hypernuclei & mesic nuclei
• Nuclear forces
• Nuclear structure & decays
• A ≤ 5
• Discrete symmetries