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Exploring high multiplicity amplitudes: the quantum mechanics analogue of the spontaneously broken case

Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step toward this problem we consider the quantum mechanical equivalent of 1→n scattering amplitudes in a spontaneously broken ϕ4-...

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Hauptverfasser: Jaeckel, Joerg (VerfasserIn) , Schenk, Sebastian (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 22 March 2019
In: Physical review
Year: 2019, Jahrgang: 99, Heft: 5
ISSN:2470-0029
DOI:10.1103/PhysRevD.99.056010
Online-Zugang:Verlag, Volltext: https://doi.org/10.1103/PhysRevD.99.056010
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.99.056010
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Verfasserangaben:Joerg Jaeckel and Sebastian Schenk

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520 |a Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step toward this problem we consider the quantum mechanical equivalent of 1→n scattering amplitudes in a spontaneously broken ϕ4-theory by extending our previous results on the quartic oscillator with a single minimum [Phys. Rev. D 98, 096007 (2018)] to transitions ⟨n|^x|0⟩ in the symmetric double-well potential with quartic coupling λ. Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form ⟨n|^x|0⟩∼exp(F(λn)/λ) in the limit of large n and λn fixed. We apply the methods of “exact perturbation theory” put forward by Serone et al. in [Phys. Rev. D 96, 021701 (2017); J. High Energy Phys. 05 (2017) 056] to obtain the exponent F and investigate its structure in the regime where tree-level perturbation theory violates unitarity constraints. We find that the resummed exponent is in agreement with unitarity and rigorous bounds derived by Bachas [Nucl. Phys. B377, 622 (1992)]. 
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