  According to Landau's Fermi liquid theory, the main properties of the
quasiparticle excitations of an electron gas are embodied in the effective mass
$m^*$, which determines the energy of a single quasiparticle, and the Landau
interaction function, which indicates how the energy of a quasiparticle is
modified by the presence of other quasiparticles. This simple paradigm
underlies most of our current understanding of the physical and chemical
behavior of metallic systems. The quasiparticle effective mass of the
three-dimensional homogeneous electron gas has been the subject of theoretical
controversy and there is a lack of experimental data. In this work, we deploy
diffusion Monte Carlo (DMC) methods to calculate $m^*$ as a function of density
for paramagnetic and ferromagnetic three-dimensional homogeneous electron
gases. The DMC results indicate that $m^*$ decreases when the density is
reduced, especially in the ferromagnetic case. The DMC quasiparticle energy
bands exclude the possibility of a reduction in the occupied bandwidth relative
to that of the free-electron model at density parameter $r_s=4$, which
corresponds to Na metal.
