Charge-symmetry breaking in the mass-4 mirror hypernuclei
In plain words
The hypernuclei $4_{\Lambda}\,\mathrm{H}$ and $4_{\Lambda}\,\mathrm{He}$ differ only by swapping one proton for a neutron, so apart from small electric effects the $\Lambda$ should be bound equally in both. The measured difference is much larger than in ordinary mirror nuclei and changes sign between the ground and excited states, and theory does not yet reproduce it reliably.
Precise statement
Define $\Delta B_{\Lambda}(J) = B_{\Lambda}(4_{\Lambda}\,\mathrm{He}) - B_{\Lambda}(4_{\Lambda}\,\mathrm{H})$ for the $0+$ ground and $1+$ excited states. STAR measured $\Delta B_{\Lambda}(0+) = 0.16 \pm 0.14\,(\mathrm{stat}) \pm 0.10\,(\mathrm{syst})\,\mathrm{MeV}$ and $\Delta B_{\Lambda}(1+) = -0.16 \pm 0.14\,(\mathrm{stat}) \pm 0.10\,(\mathrm{syst})\,\mathrm{MeV}$ (PLB 834, 137449, 2022). Determine the mechanism ($\Lambda-\Sigma0$ mixing, $\Lambda N$ to $\Sigma N$ conversion with one-pion exchange, charge-symmetry-breaking contact terms) and the implied difference between the $\Lambda p$ and $\Lambda n$ scattering lengths. Answer: an ab initio four-body calculation with a chiral YN interaction reproducing both values, with a prediction of the $\Lambda n$ scattering length.
What would settle it
Gamma-ray and decay-pion spectroscopy of both hypernuclei at the $20\,\mathrm{keV}$ level, combined with four-body calculations using chiral YN forces at next-to-next-to-leading order.
Status in the literature
Unverified note
Chiral effective field theory analyses fitted charge-symmetry-breaking contact terms to the $A = 4$ data to constrain the $\Lambda n$ interaction (Haidenbauer, Meissner, Nogga, arXiv 2107.01134, 2021), with the input data themselves uncertain at the $0.1\ \mathrm{MeV}$ level as of 2026.