  The quantum pyrochlore antiferromagnet is studied by perturbative expansions
and exact diagonalization of small clusters. We find that the ground state is a
spin-liquid state: The spin-spin correlation functions decay exponentially with
distance and the correlation length never exceeds the interatomic distance. The
calculated magnetic neutron diffraction cross section is in very good agreement
with experiments performed on Y(Sc)Mn2. The low energy excitations are
singlet-singlet ones, with a finite spin gap.
