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We report on our recent result [1] concerning in-medium $\Lambda$ isospin impurity derived from charge symmetry breking (CSB) in the mirror hypernuclei ${\rm ^4_\Lambda H}-{\rm ^4_\Lambda He}$. Using pionless effective field theory and partially conserved baryon-baryon SU(3) flavor symmetry we find that the in-medium admixture amplitude ${\cal A}_{I=1}$ in the dominantly isospin $I=0$ $\Lambda$ hyperon retains its free-space value $\approx 1.5\%$ inferred by Dalitz and von Hippel [2] and recent QCD+QED lattice calculations [3]. In agreement with recent work [4] we observe that CSB affects spin-singlet and spin-triplet $\Lambda N$ channels differently - in opposite directions, with the former dominating by an order of magnitude. This difference might be explained as a consequence of SU(3) flavor symmetry.
[1] M. Schafer, N. Barnea, A. Gal, arXiv:2202.07460v2 [nucl-th] (2022).
[2] R. H. Dalitz and F. von Hippel, Phys. Lett 10, 153 (1964).
[3] Z. R. Kordov, R. Horsley, Y. Nakamura et al. Phys. Rev. D 101, 034517 (2020).
[4] J. Haidenbauer, U.-G. Meissner, and A. Nogga, Few-Body Syst. 62, 105 (2021).
