  We study the asymmetric Hubbard model at half-filling as a generic model to
describe the physics of two species of repulsively interacting fermionic cold
atoms in optical lattices. We use Dynamical Mean Field Theory to obtain the
paramagnetic phase diagram of the model as function of temperature, interaction
strength and hopping asymmetry. A Mott transition with a region of two
coexistent solutions is found for all nonzero values of the hopping asymmetry.
At low temperatures the metallic phase is a heavy Fermi-liquid, qualitatively
analogous to the Fermi liquid state of the symmetric Hubbard model. Above a
coherence temperature, an orbital-selective crossover takes place, wherein one
fermionic species effectively localizes, and the resulting bad metallic state
resembles the non-Fermi liquid state of the Falicov-Kimball model. We compute
observables relevant to cold atom systems such as the double occupation, the
specific heat and entropy and characterize their behavior in the different
phases.
