Exploring high multiplicity amplitudes in quantum mechanics
Calculations of 1→N amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number N of final state particles. This either indicates an end of perturbative behavior, or possibly even a breakdown of the theory itself. It has recently been proposed th...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
15 November 2018
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| In: |
Physical review
Year: 2018, Jahrgang: 98, Heft: 9 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.98.096007 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevD.98.096007 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.98.096007 
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| Verfasserangaben: | Joerg Jaeckel and Sebastian Schenk |
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| 520 | |a Calculations of 1→N amplitudes in scalar field theories at very high multiplicities exhibit an extremely rapid growth with the number N of final state particles. This either indicates an end of perturbative behavior, or possibly even a breakdown of the theory itself. It has recently been proposed that in the Standard Model this could even lead to a solution of the hierarchy problem in the form of a “Higgsplosion” [1]. To shed light on this question we consider the quantum mechanical analogue of the scattering amplitude for N particle production in ϕ4 scalar quantum field theory, which corresponds to transitions ⟨N|^x|0⟩ in the anharmonic oscillator with quartic coupling λ. We use recursion relations to calculate the ⟨N|^x|0⟩ amplitudes to high order in perturbation theory. Using this we provide evidence that the amplitude can be written as ⟨N|^x|0⟩∼exp(F(λN)/λ) in the limit of large N and λN fixed. We go beyond the leading order and provide a systematic expansion in powers of 1/N. We then resum the perturbative results and investigate the behavior of the amplitude in the region where tree-level perturbation theory violates unitarity constraints. The resummed amplitudes are in line with unitarity as well as stronger constraints derived by Bachas [2]. We generalize our result to arbitrary states and powers of local operators ⟨N|^xq|M⟩ and confirm that, to exponential accuracy, amplitudes in the large N limit are independent of the explicit form of the local operator, i.e., in our case q. | ||
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