  We calculate the properties of the two-band Hubbard model using the Dynamical
Cluster Approximation. The phase diagram resembles the generic phase diagram of
the cuprates, showing a strong asymmetry with respect to electron and hole
doped regimes, in agreement with experiment. Asymmetric features are also seen
in one-particle spectral functions and in the charge, spin and d-wave pairing
susceptibility functions. We address the possible reduction of the two-band
model to a low-energy single-band one, as it was suggested by Zhang and Rice.
Comparing the two-band Hubbard model properties with the single-band Hubbard
model ones, we have found similar low-energy physics provided that the
next-nearest-neighbor hopping term t' has a significant value ($t'/t \approx
0.3$). The parameter t' is the main culprit for the electron-hole asymmetry.
However, a significant value of t' cannot be provided in a strict Zhang and
Rice picture where the extra holes added into the system bind to the existing
Cu holes forming local singlets. We notice that by considering approximate
singlet states, such as plaquette ones, reasonable values of t', which capture
qualitatively the physics of the two-band model can be obtained. We conclude
that a single-band t-t'-U Hubbard model captures the basic physics of the
cuprates concerning superconductivity, antiferromagnetism, pseudogap and
electron-hole asymmetry, but is not suitable for a quantitative analysis or to
describe physical properties involving energy scales larger than about 0.5 eV.
