Exploring high multiplicity amplitudes: the quantum mechanics analogue of the spontaneously broken case - Jaeckel, Joerg; Schenk, Sebastian (Physical review, 2019)
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)].