English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Perturbation expansions appear to be divergent series in many physicallyinteresting situations, including in quantum field theories like quantumelectrodynamics (QED) and quantum chromodynamics (QCD), where the perturbativecoefficients exhibit a factorial growth at large orders. While this feature haslittle impact on physical predictions in QED, it can have nontrivialconsequences in applications of perturbative QCD at moderate energies. Inparticular, it affects the theoretical error in the extraction of the strongcoupling $\alpha_s$ from hadronic $\tau$ decays, despite progress ofperturbative calculations available at present to four loops. We discuss a newtype of perturbative expansion for QCD correlators, which uses instead of thestandard powers of the coupling a new set of expansion functions. Thesefunctions are defined by means of an optimal conformal mapping of the Borelcomplex plane, which implements the known features of the high-order divergencein terms of the lowest Borel-plane singularities. The properties of theexpansion functions resemble those of the expanded correlators, by exhibitingin particular the singular behaviour of the correlators at $\alpha_s=0$. Weprove the good convergence properties of the new expansions on mathematicalmodels that simulate the physical polarization function for light quarks andits derivative (the Adler function), in various prescriptions ofrenormalization-group summation.

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