Fermi polaron in low-density spin-polarized neutron matter

We study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, we analyze its energy, effective mass and residue, and we compare the results obtained with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments. The calculations are performed within the Brueckner--Hartree--Fock approach using the chiral two-body nucleon-nucleon potential of Entem and Machleidt at N$^3$LO with a 500 MeV cut-off, and including only contributions from the $^1S_0$ partial wave which is the dominating one in the low-density region considered. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. Our results for the energy ($E_{\downarrow}=-0.63\,E_F$), effective mass ($m^*_{\downarrow}=1.18\,m$) and residue ($Z_{\downarrow}=0.78$) of the impurity are in very good agreement with quantum Monte Carlo calculations, showing that a spin-down neutron impurity in a low-density free Fermi gas of spin-up neutrons exhibits properties very close to those of an attractive Fermi polaron in the unitary limit.