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

Abstract

The $\Lambda$ separation energies in the mirror hypernuclei ${}_{\Lambda }^4\mathrm{H}-{}_{\Lambda }^4\mathrm{He}$ 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 $\Lambda -{\Sigma }^0$ induced in-medium admixture amplitude ${\mathcal{A}}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0$ $\Lambda$ hyperon. Our results confirm the free-space value ${\mathcal{A}}_{I=1}^{(0)}$ 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.

arXiv comment5 pages, 4 figures, 1 table, to be submitted for publication. v2: slightly shortened, submitted for publication. v3: slightly revised in response to referee remarks. v4: as published in PRC 106 (2022) L031001. v5: inessential typos corrected in eqs.(4,5,9) here and in the latest PRC published version

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