  A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is
formulated and used for the description of superconducting (SC) ground state in
the two-dimensional Hubbard model with electron-transfer amplitudes t (and t')
between nearest (and next-nearest) neighbors. The method is numerically very
efficient and allows for a detailed analysis of the phase diagram as a function
of all relevant parameters (U, \delta, t') and a determination of the
kinetic-energy driven pairing region. SC states appear only for substantial
interactions, U/t > 3, and for not too large hole doping, \delta < 0.32 for t'
= 0.25 t; this upper critical doping value agrees well with experiment for the
cuprate high-temperature superconductors. We also obtain other important
features of the SC state: (i) the SC gap at the Fermi surface resembles
$d_{x^2-y^2}$-wave only around the optimal doping and the corrections to this
state are shown to arise from the longer range of the pairing; (ii) the nodal
Fermi velocity is almost constant as a function of doping and agrees
quantitatively with the experimental results; (iii) the SC transition is driven
by the kinetic-energy lowering for low doping and strong interactions.
