In physics, a renormalon (a term suggested by 't Hooft[1]) is a particular source of divergence seen in perturbative approximations to quantum field theories (QFT).
When a formally divergent series in a QFT is summed using Borel summation, the associated Borel transform of the series can have singularities as a function of the complex transform parameter.
Associated with such singularities, renormalon contributions are discussed in the context of quantum chromodynamics (QCD)[2] and usually have the power-like form
Perturbation series in quantum field theory are usually divergent as was firstly indicated by Freeman Dyson.
-th order contribution of perturbation theory into any quantity can be evaluated at large
in the saddle-point approximation for functional integrals and is determined by instanton configurations.
Lautrup[5] has noted that there exist individual diagrams giving approximately the same contribution.
In principle, it is possible that such diagrams are automatically taken into account in Lipatov's calculation, because its interpretation in terms of diagrammatic technique is problematic.
However, 't Hooft put forward a conjecture that Lipatov's and Lautrup's contributions are associated with different types of singularities in the Borel plane, the former with instanton ones and the latter with renormalon ones.
Among the essential contributions one should mention the application of the operator product expansion, as was suggested by Parisi.
theory and a general criterion for their existence was formulated[8] in terms of the asymptotic behavior of the Gell-Mann–Low function