Nonperturbative effects in quarkonia associated with large orders in perturbation theory

We show that the perturbation series for quarkonia energies diverges at large orders. This results in a perturbative ambiguity in the energy that scales as e−2naΛ, where n is the principal quantum number, a is the Bohr radius, and Λ is the QCD scale parameter. This ambiguity is associated with nonperturbative contribution to the energy from distances of order Λ−1 and greater. This contribution is separate from that of the gluon condensate.