Charge symmetry breaking in $\Lambda$ hypernuclei revisited

TL;DR

This paper revisits charge symmetry breaking in $ ext{Lambda}$ hypernuclei using a strong-interaction coupling model, providing improved theoretical estimates that better align with experimental data and explaining previous observational failures.

Contribution

It extends a schematic $ ext{Lambda N} ightleftharpoons ext{Sigma N}$ coupling model to $p$-shell hypernuclei, offering refined CSB predictions consistent with experimental observations.

Findings

CSB effects are around 0.25 MeV for $A=4$ hypernuclei.

Smaller, mostly negative binding energy differences in $A=7-10$ hypernuclei.

CSB reduces the expected $ ext{Lambda}$ hypernuclei doublet splitting by ~30 keV.

Abstract

The large charge symmetry breaking (CSB) implied by the $\Lambda$ binding energy difference $\Delta B^{4}_{\Lambda}(0^+_{\rm g.s.})\equiv B_{\Lambda}(_{\Lambda}^4$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 $\Delta B^{4}_{\Lambda} (0^+_{\rm g.s.})\sim 0.25$ 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 $_{~\Lambda}^{10}$B g.s. doublet splitting anticipated from the hyperon-nucleon strong-interaction spin dependence, thereby explaining the persistent experimental failure to observe the $2^-_{\rm exc}\to 1^-_{\rm g.s.}$ $\gamma$-ray transition.