Charge symmetry breaking in the A=4 hypernuclei

Charge symmetry breaking (CSB) in the $Λ$-nucleon strong interaction generates a charge dependence of $Λ$ separation energies in mirror hypernuclei, which in the case of the $A=4$ mirror hypernuclei $0^+$ ground states is sizable, $ΔB^{J=0}_Λ\equiv B^{J=0}_Λ (_Λ^4{\rm He}) -B^{J=0}_Λ(_Λ^4{\rm H})=230\pm 90$ keV, and of opposite sign to that induced by the Coulomb repulsion in light hypernuclei. Recent ab-initio calculations of the ($_Λ^4{\rm H},{_Λ^4{\rm He}}$) mirror hypernuclei $0^+_{\rm g.s.}$ and $1^+_{\rm exc}$ levels have demonstrated that a $Λ- Σ^0$ mixing CSB model due to Dalitz and von Hippel (1964) is capable of reproducing this large value of $ΔB^{J=0}_Λ$. These calculations are discussed here with emphasis placed on the leading-order chiral EFT hyperon-nucleon strong-interaction Bonn-Juelich potential model used and the no-core shell-model calculational scheme applied. The role of one-pion exchange in producing sizable CSB level splittings in the $A=4$ mirror hypernuclei is discussed.

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