Nonperturbative Effects in Quarkonia Associated with Large Orders in Perturbation Theory
Martin C. Smith, T. Stelzer, S. Willenbrock
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.
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