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Modern Approach to Analyticity

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Functional Analysis and Optimization Methods in Hadron Physics

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

In this chapter we discuss the status of analyticity within the Standard Model of particle physics. First, the proof given by Oehme for the analytic properties of the hadronic amplitudes in quantum chromodynamics (QCD) is presented at a qualitative level. We then review the recent progress in modern dispersion theory, in connection with the developments in chiral perturbation theory and lattice QCD, and emphasize the role of analytic continuation for relating the predictions of perturbative QCD to low-energy physical observables. Finally, we introduce functional analysis techniques as alternatives to the standard dispersion relations for implementing in an optimal way the available theoretical or experimental input. Two examples involving hadronic form factors and perturbative QCD are given for illustration.

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Notes

  1. 1.

    For a recent review see: J. A. Oller, A Brief Introduction to Dispersion Relations—With Modern Applications, (SpringerBrief in Physics, 2019).

  2. 2.

    The expansion (2.14) is actually divergent, the coefficients \(c_{n,1}\) growing factorially as n! at large n. We shall discuss in more detail this aspect in Chap. 6.

  3. 3.

    We shall discuss the origin and the expression of the duality-violating terms in Sect. 6.1.

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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). Modern Approach to Analyticity. In: Functional Analysis and Optimization Methods in Hadron Physics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-18948-8_2

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