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We report the results of the computation of the order $(k_{\rm F}a_0)^2$correction, where $k_{\rm F}=3\pi^2\rho$ is the Fermi wave vector and $a_0$ the$s$-wave scattering length of the repulsive interaction, to the ground-stateenergy of a mixture of oppositely polarized $N_a$ spin $1/2$ fermions $a$ ofmasses $m_a$ and $N_b$ spin $1/2$ fermions $b$ of masses $m_b$ ($\rho=N/V$,$N=N_a+N_b$). It is shown that the results of the paper \cite{FraPil} in whichthe same correction has been computed entirely numerically, using a moretraditional approach, can be easily and semianalytically reproduced using theeffective field theory technique.

On the ground-state energy of a mixture of two different oppositely polarized fermionic gases