Ultraviolet renormalons in abelian gauge theories

Abstract

We analyze the large-order behaviour in perturbation theory of classes of diagrams with an arbitrary number of chains (i.e. photon lines, dressed by vacuum polarization insertions). We derive explicit formulae for the leading and subleading divergence as $n\to \infty$, and a complete result for the vacuum polarization at the next-to-leading order in $1/N_f$. In general, diagrams with more chains yield stronger divergence. We define an analogue of the familiar diagrammatic $R$-operation, which extracts ultraviolet renormalon counterterms as insertions of higher-dimension operators. We then use renormalization group equations to sum the leading $(\ln n/N_f{)}^k$-corrections to all orders in $1/N_f$ and find the asymptotic behaviour in $n$ up to a constant that must be calculated explicitly order by order in $1/N_f$.

61 pages, LATEX, 10 figures as uu-decoded file

References in corpus (4)

• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• More on ambiguities in the pole mass
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Cited by in corpus (14)

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• On the role of power expansions in quantum field theory
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• Large $N_f$ quantum field theory
• Low-Energy QCD and Ultraviolet Renormalons
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Large-order Behaviour of the QCD Adler D-function in Planar Approximation
• On Renormalons and Landau Poles in Gauge Field Theories
• Ambiguities in QED: Renormalons versus Triviality
• The Physics of the Ultraviolet Renormalon
• The scalar gluonium correlator: large-beta_0 and beyond
• High order corrections to the Renormalon