TY - JOUR

T1 - Ultraviolet renormalon reexamined

AU - Vainshtein, A. I.

AU - Zakharov, V. I.

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.54.4039

DO - 10.1103/PhysRevD.54.4039

M3 - Article

AN - SCOPUS:0001384398

VL - 54

SP - 4039

EP - 4048

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

ER -