  A detailed study of charged current quasielastic neutrino and antineutrino
scattering cross sections on a $^{12}$C target with no pions in the final state
is presented. The initial nucleus is described by means of a realistic spectral
function $S(p,{\cal E})$ in which nucleon-nucleon correlations are implemented
by using natural orbitals through the Jastrow method. The roles played by these
correlations and by final-state interactions are analyzed and discussed. The
model also includes the contribution of weak two-body currents in the
two-particle two-hole sector, evaluated within a fully relativistic Fermi gas.
The theoretical predictions are compared with a large set of experimental data
for double-differential, single-differential and total integrated cross
sections measured by the MiniBooNE, MINER$\nu$A and T2K experiments. Good
agreement with experimental data is found over the whole range of neutrino
energies. The results are also in global good agreement with the predictions of
the superscaling approach, which is based on the analysis of electron-nucleus
scattering data, with only a few differences seen at specific kinematics.
