Nonperturbative Effects in Quarkonia Associated with Large Orders in Perturbation Theory

Abstract

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^(-1/a*Lambda) where a is the Bohr radius of quarkonium and Lambda is the QCD scale parameter. This ambiguity is associated with a nonperturbative contribution to the energy from distances of order 1/Lambda and greater. This contribution is separate from that of the gluon condensate.