Conformal mappings in perturbative QCD
Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, Magurele, 077125, Bucharest, Romania
Accepted: 26 July 2021
Published online: 12 August 2021
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable which performs the conformal mapping of the cut Borel plane onto the unit disk. We write down the expression of the conformal mapping for the most general location of the singularities of the Borel transform and review the properties of the corresponding expansions of the correlators. Unlike the standard perturbative expansions, which are divergent, the modified expansions have a tamed behaviour at large orders and may even converge under some conditions. On the other hand, the expansion functions exhibit nonperturbative features similar to those of the expanded function. Using these properties, it was suggested recently that the expansions based on the conformal mapping of the Borel plane may provide an alternative to the standard OPE. We briefly review the arguments in favour of this conjecture and discuss the application of the method to the Adler function for massless quarks and the static quark self-energy calculated in lattice QCD.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021