Excitation spectra of CΞ15 and BeΞ12 calculated with a <mml:math xmlns:mml="http…

Background:The accumulation of experimental data on Ξ hypernuclei has enabled testing the ΞN interactions derived from first-principles lattice QCD simulations through many-body calculations.Purpose:Based on the interactions derived from lattice QCD simulations, we calculate the spectrum of the ¹⁴N+Ξ^- states in _Ξ¹⁵C as well as that of the ¹²C+Ξ^- states in _Ξ¹³B and compare with observed data from emulsion experiments. In addition, we predict the spectrum of _Ξ¹²Be (¹¹B+Ξ^-) using the same interaction.Methods:Through the G-matrix calculations, we derive low-energy effective interactions from lattice QCD potentials, where we introduce odd-parity potentials based on the meson-exchange picture because they have not been obtained from lattice QCD simulations. Employing these interactions, we carry out molecular dynamics model calculations to obtain the spectra of _Ξ¹³B, _Ξ¹⁵C, and _Ξ¹²Be.Results:The s-wave states of Ξ^- in _Ξ¹⁵C are bound in the range of 5 to 10 MeV, while the p-wave states are in the range of 0 to 2 MeV. The same Hamiltonian predicts the bound s-wave states of _Ξ¹²Be in the range of 3 to 5 MeV. The obtained spectra show small spin-spin splitting and conversion widths.Conclusions:The results for _Ξ¹³B and _Ξ¹⁵C are consistent with many of the experimental data, highlighting the capabilities of lattice QCD simulations. The binding of _Ξ¹²Be is deep enough to be observed by spectroscopy experiments. The difference between the lattice QCD and the meson-exchange models lies in the spin-spin splitting and conversion widths, underlining the importance of observations.