The $\mathrm{\Lambda }$ and $\mathrm{\Sigma }$ single-particle potentials in infinite nuclear matter are analyzed within a recently established chiral hyperon-nucleon ($YN$) interaction up to ${\mathrm{N}}^2\mathrm{LO}$ in combination with a nucleon-nucleon interaction derived in the same scheme. The self-consistent Brueckner-Hartree-Fock method with the continuous choice of the single-particle potential is employed. It is found that the $\mathrm{\Lambda }$ single-particle potential is comparable to the results achieved with the NLO $YN$ interaction from 2019. The resulting $\mathrm{\Sigma }$ potential becomes more attractive compared to the previous NLO results due to the constraint from the recent $\mathrm{\Sigma }N$ differential cross section data measured in the J-PARC E40 experiment. An estimate of the theoretical uncertainty of the single-particle potentials is provided in terms of the truncation error in the chiral expansion.

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• Nuclear forces
• Nuclear matter
• Hyperons