Conformal mappings in perturbative QCD

Abstract

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.

version accepted for publication in EPJST. arXiv admin note: text overlap with arXiv:2006.16605

References in corpus (10)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Conformal mapping of the Borel plane: going beyond perturbative QCD
• Resurgence of the QCD Adler function
• The case for duality violations in the analysis of hadronic $\tau$ decays
• Higher-order behaviour of two-point current correlators

Cited by in corpus (1)

• On the difference between Fixed-Order and Contour-Improved Perturbation Theory