  We reexamine whether the essence of high-Tc 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 dx2-y2 wave symmetry in the ground state at distance r
decays essentially as inverse cubic of r. The upper bound of the correlation at
long distances estimated by this unbiased method is 0.001, 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-Tc
superconductivity.
