Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1994-04-11
Phys.Rev.Lett. 73 (1994) 1207-1210; Erratum-ibid. 75 (1995) 3588
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTex, 18 pages, 5 figures. Some numerical coefficients are corrected once more
Scientific paper
10.1103/PhysRevLett.75.3588
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 $k^2$ of order $Q^2e^n$ where $Q$ is external momentum, $e$ is the base of natural logs and $n$ is the order of perturbation theory considered. To evaluate the UV renormalon we develop formalism of operator product expansion (OPE) which utilizes the observation that $k^2\gg Q^2$. When applied to the simplest graphs the formalism reproduces the known results in a compact form. In more generality, 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 $\ln k^2$ their contribution is enhanced by combinatorial factors.
Vainshtein A. I.
Zakharov Valentin I.
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