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Functional Analysis and Optimization Methods in Perturbative QCD

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Functional Analysis and Optimization Methods in Hadron Physics

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Abstract

In this chapter we first show that ideas from hyperasymptotics can be used to infer the existence of terms additional to the usual operator product expansions (OPE) of QCD correlators. A connection between these quark-hadron duality-violating terms and the singularities of the Borel-Laplace transform in the Borel plane is emphasized. We then discuss a method based on functional analysis for testing the presence of duality violation from experimental data. Finally, an alternative way to go beyond finite-order perturbation theory, by a modified perturbative expansion based on the conformal mapping of the Borel plane, is briefly discussed.

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Notes

  1. 1.

    In mathematical language, we say that the Adler function is not Borel summable. The Borel nonsummability results also from the structure of the singularities of D near the origin of the \(a_s\) complex plane, obtained in [1, 2].

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Authors and Affiliations

  1. Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

    Irinel Caprini

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  1. Irinel Caprini
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Correspondence to Irinel Caprini .

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Caprini, I. (2019). Functional Analysis and Optimization Methods in Perturbative QCD. In: Functional Analysis and Optimization Methods in Hadron Physics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-18948-8_6

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