Is the zero-point energy a source of the cosmological constant?

We discuss how we remove a huge discrepancy between the theory of a cosmological constant, due to the zero-point energies of matter fields, and the observation. The technique of dimensional regularization plays a decisive role. We eventually reach the desired behavior of the vacuum densities falling off like t^{-2}, allowing us to understand how an extremely small result comes about naturally. As a price, however, the zero-point energy vacuum fails to act as a true cosmological constant. Its expected role responsible for the observed accelerating universe is then to be inherited by the gravitational scalar field, dark energy, as we suggest in the scalar-tensor theory.