Does simple two-dimensional Hubbard model account for high-T _c superconductivity in copper oxides?

We reexamine whether the essence of high-T _c superconductivity is contained in doped Hubbard models on the square lattice by using recently developed pre-projected Gaussian-basis Monte Carlo method. The superconducting correlations of the d _x2-y2 wave symmetry in the ground state at distance r decays essentially as r ^-3. The upper bound of the correlation at long distances estimated by this unbiased method is 10 ^-3, indicating that recent extensions of dynamical mean-field theories and variational methods yielded at least an order of magnitude overestimates of it. The correlations are too weak for the realistic account of the cuprate high-T _c superconductivity.