Abstract
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 scattering amplitudes in a spontaneously broken -theory by extending our previous results on the quartic oscillator with a single minimum [Phys. Rev. D 98, 096007 (2018)] to transitions in the symmetric double-well potential with quartic coupling . Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form in the limit of large and 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 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)].
- Received 3 January 2019
DOI:https://doi.org/10.1103/PhysRevD.99.056010
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Published by the American Physical Society