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Perturbative expansions in QCD improvrd by conformal mappings of the Borel plane

Caprini, I and Fischer, J and Abbas, G and Ananthanarayan, B (2018) Perturbative expansions in QCD improvrd by conformal mappings of the Borel plane. [Book Chapter]

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Perturbative expansions appear to be divergent series in many phys- ically 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 or- ders. While this feature has little impact on physical predictions in 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 αs from hadronic τ 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. These functions are defined by means of an optimal conformal mapping of the Borel complex plane, which implements the known features of the high-order divergence in terms of the lowest Borelplane singularities. The properties of the expansion functions resemble those of the expanded correlators, by exhibiting in particular the singular behaviour of the correlators at αs = 0. We prove the good convergence properties of the new expansions on mathematical models that simulate the physical polarization function for light quarks and its derivative (the Adler function), in various prescriptions of renormalization-group summation.

Item Type: Book Chapter
Publication: Perturbation Theory: Advances in Research and Applications
Series.: Physics Research and Technology
Publisher: Nova Science Publishers, Inc.
Additional Information: The copyright for this article belongs to the Nova Science Publishers, Inc.
Keywords: Borel summation; Conformal mappings; Divergent series; Perturbation theory; Quantum chromodynamics
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 23 Aug 2022 10:32
Last Modified: 23 Aug 2022 10:32
URI: https://eprints.iisc.ac.in/id/eprint/76102

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