  Central and spin-spin potentials for charmonium, constructed from
Nambu-Bethe-Salpeter amplitudes in lattice simulations of full QCD, are matched
with results from perturbative QCD at an appropriate distance scale. This
matching is made possible by defining the perturbative potentials through
Fourier transforms with a low-momentum cutoff. The central (spin-independent)
potential is compared with potentials derived from an expansion in powers of
the inverse quark mass. A well-controlled continuation of the charmonium
spin-spin potential from lattice QCD to short distances is performed. The mass
splittings of the charmonium singlet and triplet states below the open charm
threshold, obtained from the matched spin-spin potential, are in good agreement
with the experimental values.
