Properties of hyperons in nuclear matter from chiral hyperon-nucleon interactions at next-to-next-to-leading order

The $\Lambda$ and $\Sigma$ single-particle potentials in infinite nuclear matter are analyzed within a recently established chiral hyperon-nucleon ($YN$) interaction up to N$^2$LO in combination with an 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 $\Lambda$ single-particle potential is comparable to the results achieved with the NLO $YN$ interaction from 2019. The resulting $\Sigma$ potential becomes more attractive compared to the previous NLO results due to the constraint from the recent $\Sigma N$ 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.