On the Ground-state Energy of a Mixture of Two Different Oppositely Polarized Fermionic Gases

We report the results of the computation of the order ( k F a 0 ) 2 correction, where k F = 3 π 2 ρ is the Fermi wave vector and a 0 the s -wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized N a spin 1 / 2 fermions a of masses m a and N b spin 1 / 2 fermions b of masses m b ( ρ = N/V , N = N a + N b ). It is shown that the results of the paper [1] in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using the effective field theory technique.