Charge symmetry breaking in $Λ$ hypernuclei revisited
The large charge symmetry breaking (CSB) implied by the $Λ$ binding energy difference $ΔB^{4}_Λ(0^+_{\rm g.s.})\equiv B_Λ(_Λ^4$He)$-$$B_Λ(_Λ^4$H) = 0.35$\pm$0.06 MeV of the $A=4$ mirror hypernuclei ground states, determined from emulsion studies, has defied theoretical attempts to reproduce it in terms of CSB in hyperon masses and in hyperon-nucleon interactions, including one pion exchange arising from $Λ-Σ^0$ mixing. Using a schematic strong-interaction $ΛN\leftrightarrowΣN$ coupling model developed by Akaishi and collaborators for $s$-shell $Λ$ hypernuclei, we revisit the evaluation of CSB in the $A=4$ $Λ$ hypernuclei and extend it to $p$-shell mirror $Λ$ hypernuclei. The model yields values of $ΔB^{4}_Λ (0^+_{\rm g.s.})\sim 0.25$ MeV. Smaller size and mostly negative $p$-shell binding energy differences are calculated for the $A=7-10$ mirror hypernuclei, in rough agreement with the few available data. CSB is found to reduce by almost 30 keV the 110 keV $_{~Λ}^{10}$B g.s. doublet splitting anticipated from the hyperon-nucleon strong-interaction spin dependence, thereby explaining the persistent experimental failure to observe the $2^-_{\rm exc}\to 1^-_{\rm g.s.}$ $γ$-ray transition.