Charge symmetry breaking in $\Lambda$ hypernuclei revisited

Abstract

The large charge symmetry breaking (CSB) implied by the $\Lambda$ binding energy difference $\Delta B_{\Lambda }^4(0_{g.s.}^{+})\equiv B_{\Lambda }{(}_{\Lambda }^4$He)$-$$B_{\Lambda }{(}_{\Lambda }^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 $\Lambda -{\Sigma }^0$ mixing. Using a schematic strong-interaction $\Lambda N\leftrightarrow \Sigma N$ coupling model developed by Akaishi and collaborators for $s$-shell $\Lambda$ hypernuclei, we revisit the evaluation of CSB in the $A=4$ $\Lambda$ hypernuclei and extend it to $p$-shell mirror $\Lambda$ hypernuclei. The model yields values of $\Delta B_{\Lambda }^4(0_{g.s.}^{+})\sim 0.25$ 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 ${}_{\Lambda }^{10}$B g.s. doublet splitting anticipated from the hyperon-nucleon strong-interaction spin dependence, thereby explaining the persistent experimental failure to observe the $2_{\mathrm{exc}}^{-}\to 1_{g.s.}^{-}$ $\gamma$-ray transition.

arXiv commenta few clarifying statements added to v2; matches published PLB version plus a note added after publication on p.13

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