Polaronic and dressed molecular states in orbital Feshbach resonances

We consider the impurity problem in an orbital Feshbach resonance (OFR), with a single excited clock state $|e\uparrow\rangle$ atom immersed in a Fermi sea of electronic ground state $|g\downarrow\rangle$. We calculate the polaron effective mass and quasi-particle residue, as well as the polaron to molecule transition. By including one particle-hole excitation in the molecular state, we find significant correction to the transition point. This transition point moves toward the BCS side for increasing particle densities, which suggests that the corresponding many-body physics is similar to a narrow resonance.