The recently developed hadron resonance gas model with multicomponent hard-core repulsion is used to address and resolve the long standing problem to describe the light nuclear cluster multiplicities including the hyper-triton measured by the STAR Collaboration, known as the hyper-triton chemical freeze-out puzzle. An improved description for the hadronic and light nuclear cluster data measured by STAR at the collision energy $$\sqrt{s_{NN}} =200$$
s
NN
=
200
GeV and by ALICE at $$\sqrt{s_{NN}} =2.76$$
s
NN
=
2.76
TeV is obtained. This is achieved by applying a new strategy of analyzing the light nuclear cluster data and by using the value for the hard-core radius of the (anti-)$$\varLambda $$
Λ
hyperons found in earlier work. One of the most striking results of the present work is that for the most probable scenario of chemical freeze-out for the STAR energy the obtained parameters allow to simultaneously reproduce the values of the experimental ratios $$S_3$$
S
3
and $${\overline{S}}_3$$
S
¯
3
which were not included in the fit.
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