Ab initio calculation of charge symmetry breaking in $A=7$ and $8$ $\Lambda$-hypernuclei

Abstract

The separation energies of the isospin triplet ${}_{\Lambda }^7\mathrm{He}$, ${}_{\Lambda }^7\mathrm{L}{\mathrm{i}}^{\ast }$, ${}_{\Lambda }^7$Be, and the $T=1/2$ doublet ${}_{\Lambda }^8$Li, ${}_{\Lambda }^8$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 $\Lambda$N channel, whose strength has been fixed to the experimentally known difference of the $\Lambda$ separation energies of the mirror hypernuclei ${}_{\Lambda }^4\mathrm{He}$ and ${}_{\Lambda }^4\mathrm{H}$. 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 case of the $A=8$ doublet, the computed CSB is somewhat larger than the available experimental value. Using other experimental input for $A=4$ can change this prediction moving it closer to experiment.

arXiv comment11 pages, 4 tables

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