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

TL;DR

This study uses ab initio no-core shell model calculations with chiral effective field theory potentials to analyze charge symmetry breaking effects in $A=7$ and $8$ hypernuclei, comparing predictions with experimental data.

Contribution

It introduces a detailed ab initio calculation of charge symmetry breaking in $A=7$ and $8$ hypernuclei using chiral EFT potentials, including the leading CSB interaction.

Findings

CSB effects in $A=7$ hypernuclei are small and match experimental uncertainties.

Predicted CSB in $A=8$ hypernuclei is larger than experimental values.

Adjusting input data for $A=4$ hypernuclei can improve the agreement with experiments.

Abstract

The separation energies of the isospin triplet $^7_\Lambda\mathrm{He}$, $^7_\Lambda \mathrm{Li^{*}}$, $^7_\Lambda$Be, and the $T=1/2$ doublet $^8_\Lambda$Li, $^8_\Lambda$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 $^4_\Lambda \mathrm{He}$ and $^4_\Lambda \mathrm{H}$. 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.