Spin-independent effective mass in a valley-degenerate electron system

In a generic spin-polarized Fermi liquid, the masses of spin-up and spin-down electrons are expected to be different and to depend on the degree of polarization. This expectation is not confirmed by the experiments on two-dimensional heterostructures. We consider a model of an N-fold degenerate electron gas. It is shown that in the large-N limit, the mass is enhanced via a polaronic mechanism of emission or absorption of virtual plasmons. As plasmons are classical collective excitations, the resulting mass does not depend on N, and thus on polarization, to the leading order in 1/N. We evaluate the 1/N corrections and show that they are small even for N=2.