Ultraviolet renormalon reexamined

We consider large-order perturbative expansions in QED and QCD. The coefficients of the expansions are known to be dominated by the so-called ultraviolet (UV) renormalons which arise from inserting a chain of vacuum-polarization graphs into photonic (gluonic) lines. In large orders the contribution is associated with virtual momenta k2 of order Q2en where Q is the external momentum, e is the base of natural logs, and n is the order of the perturbation theory considered. To evaluate the UV renormalon we develop a formalism of operator product expansion (OPE) which utilizes the observation that k2>Q2. When applied to the simplest graphs the formalism reproduces the known results in a compact form. More generally, the formalism reveals the fact that the class of the renormalon-type graphs is not well defined. In particular, graphs with extra vacuum-polarization chains are not suppressed. The reason is that while inclusion of extra chains lowers the power of lnk2 their contribution is enhanced by combinatorial factors. copyright 1996 The American Physical Society