Renormalons

Renormalons are singularities in the Borel transform of perturbative expansions in quantum field theories, most prominently in quantum chromodynamics (QCD). They appear as poles or branch cuts in the Borel plane and reflect the factorial growth of perturbative coefficients induced by the running of the coupling and the integration over different momentum scales. As such, renormalons are a manifestation of the asymptotic nature of perturbation theory and signal ambiguities in resumming the series.

Renormalons are categorized as infrared (IR) or ultraviolet (UV) depending on the momentum region that dominates the corresponding Feynman diagrams. IR renormalons arise from low-momentum contributions and are tied to non-perturbative power corrections in 1/Q^p; UV renormalons stem from high-momentum regions and affect the perturbative expansion differently. The presence of renormalons implies that certain quantities have intrinsic ambiguities of order (Lambda_QCD/Q)^p, which must be compensated by non-perturbative terms in a complete description, e.g., via the operator product expansion.

In practice, renormalons constrain precision in QCD predictions. A well-known example is the pole mass of a heavy quark, which exhibits an infrared renormalon ambiguity of order Lambda_QCD, motivating the use of short-distance mass definitions. Renormalons also influence sums over perturbative series for hadronic tau decays and other observables, guiding resummation strategies and the interpretation of power corrections. Methods to handle renormalons include Borel summation with principal value prescriptions and the combination of perturbative results with non-perturbative matrix elements.