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 [Formula presented] of order [Formula presented] where [Formula presented] is the external momentum, [Formula presented] is the base of natural logs, and [Formula presented] 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 [Formula presented]. 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 [Formula presented] their contribution is enhanced by combinatorial factors.