Exploring high multiplicity amplitudes: the QM 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 towards this problem we consider the quantum mechanical equivalent of
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
29 Nov 2018
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| In: |
Arxiv
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| Online-Zugang: | Verlag, Volltext: http://arxiv.org/abs/1811.12116
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| Verfasserangaben: | Joerg Jaeckel and Sebastian Schenk |
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| 245 | 1 | 0 | |a Exploring high multiplicity amplitudes |b the QM analogue of the spontaneously broken case |c 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 towards this problem we consider the quantum mechanical equivalent of |1 \to n$ scattering amplitudes in a spontaneously broken $\phi^4$-theory by extending our previous results on the quartic oscillator with a single minimum to transitions $\langle n \lvert \hat{x} \rvert 0 \rangle$ in the symmetric double-well potential with quartic coupling $\lambda$. Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form $\langle n \lvert \hat{x} \rvert 0 \rangle \sim \exp \left( F (\lambda n) / \lambda \right)$ in the limit of large $n$ and $\lambda n$ fixed. We apply the methods of "exact perturbation theory" put forward by Serone et al. 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. | ||
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| 650 | 4 | |a High Energy Physics - Theory | |
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