Ab initio calculation of charge-symmetry breaking in A=7 and 8 Λ hypernuclei

The $\mathrm{\ensuremath{\Lambda}}$ separation energies of the isospin triplet $_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{He}, _{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{Li}^{*}, _{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{Be}$, and the $T=1/2$ doublet $_{\mathrm{\ensuremath{\Lambda}}}^{8}\mathrm{Li}, _{\mathrm{\ensuremath{\Lambda}}}^{8}\mathrm{Be}$ are investigated within the no-core shell model. Calculations are performed based on a hyperon-nucleon potential derived from chiral effective field theory at next-to-leading order. The potential includes the leading charge-symmetry breaking (CSB) interaction in the $\mathrm{\ensuremath{\Lambda}}N$ channel, whose strength has been fixed to the experimentally known difference of the $\mathrm{\ensuremath{\Lambda}}$ separation energies of the mirror hypernuclei $_{\mathrm{\ensuremath{\Lambda}}}^{4}\mathrm{He}$ and $_{\mathrm{\ensuremath{\Lambda}}}^{4}\mathrm{H}$. It turns out that the CSB predicted for the $A=7$ systems is small and agrees with the splittings deduced from the empirical binding energies within the experimental uncertainty. In the case of the $A=8$ doublet, the computed CSB is somewhat larger than the available experimental value.