Perturbative Expansions in QCD Improved by Conformal Mappings of the Borel Plane

Understand

Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients exhibit a factorial growth at large orders.

• While this feature has little impact on physical predictions in QED, it can have nontrivial consequences in applications of perturbative QCD at moderate energies.
• In particular, it affects the theoretical error in the extraction of the strong coupling $\alpha_s$ from hadronic $\tau$ decays, despite progress of perturbative calculations available at present to four loops.
• We discuss a new type of perturbative expansion for QCD correlators, which uses instead of the standard powers of the coupling a new set of expansion functions.