  The possible heavy fermion superconductivity is carefully reexamined in the
two-dimensional Kondo lattice model with an antiferromagnetic Heisenberg
superexchange between local magnetic moments. In order to establish an
effective mean field theory in the limit of the paramagnetic heavy Fermi liquid
and near the half-filling case, we find that the spinon singlet pairing from
the local antiferromagnetic short-range correlations can reduce the ground
state energy substantially. In the presence of the Kondo screening effect, the
Cooper pairs between the conduction electrons is induced. Depending on the
ratio of the Heisenberg and the Kondo exchange couplings, the resulting
superconducting state is characterized by either a d-wave nodal or d-wave
nodeless state, and a continuous phase transition exists between these two
states. These results are related to some quasi-two dimensional heary fermion
superconductors.
