In-medium $\mathrm{\Lambda }N$ interactions with leading order covariant chiral hyperon/nucleon-nucleon forces

In-medium $\mathrm{\Lambda }N$ interactions are crucial in hypernuclei and neutron star physics. In this work, we study the in-medium $\mathrm{\Lambda }N$ interaction within the relativistic Brueckner-Hartree-Fock (RBHF) framework, employing the leading-order covariant chiral hyperon/nucleon-nucleon forces for the first time. We demonstrate that a consistent description of both the experimental cross-section data and the `empirical value’ of the $\mathrm{\Lambda }$ single-particle potential can be achieved. This contrasts with the majority of studies in the non-relativistic framework, where higher-order two-body chiral forces are typically required. This study offers a new perspective on the in-medium $\mathrm{\Lambda }N$ interactions, urgently needed in relativistic $\mathit{\text{ab}}\mathit{\text{initio}}$ hypernuclear physics studies.