Charge symmetry breaking (CSB) in the $\Lambda$-nucleon strong interaction generates a charge dependence of $\Lambda$ 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 ($_{ \Lambda}^4{ \rm H},{ _{ \Lambda}^4{ \rm He}}$) mirror hypernuclei $0^+_{ \rm g.s.}$ and $1^+_{ \rm exc}$ levels have demonstrated that a $\Lambda - \Sigma^0$ mixing CSB model due to Dalitz and von Hippel (1964) is capable of reproducing this large value of $\Delta B^{ J=0}_{ \Lambda}$. 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.
Categories: nucl-th hep-ph nucl-ex