AbstractWe utilize the experimentally known difference of the $$\varLambda $$
Λ
separation energies of the mirror hypernuclei $${^4_\varLambda \mathrm{He}}$$
Λ
4
He
and $${^4_\varLambda \mathrm{H}}$$
Λ
4
H
to constrain the $$\varLambda $$
Λ
-neutron interaction. We include the leading charge-symmetry breaking (CSB) interaction into our hyperon-nucleon interaction derived within chiral effective field theory at next-to-leading order. In particular, we determine the strength of the two arising CSB contact terms by a fit to the differences of the separation energies of these hypernuclei in the $$0^+$$
0
+
and $$1^+$$
1
+
states, respectively. By construction, the resulting interaction describes all low energy hyperon-nucleon scattering data, the hypertriton and the CSB in $${^4_\varLambda \mathrm{He}}$$
Λ
4
He
-$${^4_\varLambda \mathrm{H}}$$
Λ
4
H
accurately. This allows us to provide first predictions for the $$\varLambda $$
Λ
n scattering lengths, based solely on available hypernuclear data.
Charge symmetry breaking as a probe for the real part ofη-nucleus scattering lengths