Charge symmetry breaking in the A=4 hypernuclei

Charge symmetry breaking (CSB) in the $\mathrm{\Lambda }$-nucleon strong interaction generates a charge dependence of $\mathrm{\Lambda }$ separation energies in mirror hypernuclei, which in the case of the $A=4$ mirror hypernuclei $0^{+}$ ground states is sizable, $\Delta B^{J=0}{\Lambda}\equiv B^{J=0}{\Lambda} ({\Lambda}^4{\rm He}) -B^{J=0}{\Lambda}({\Lambda}^4{\rm H})=230\pm 90$ keV, and of opposite sign to that induced by the Coulomb repulsion in light hypernuclei. Recent ab-initio calculations of the (${\Lambda}^4{\rm H},{{\Lambda}^4{\rm He}}$)mirrorhypernuclei$0^+{\rm g.s.}$and$1^+_{\rm exc}$levelshavedemonstratedthata$\Lambda - \Sigma^0$ mixing CSB model due to Dalitz and von Hippel (1964) is capable of reproducing this large value of $\mathrm{\Delta }{B}_{\mathrm{\Lambda }}^{J=0}$. 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.