The Breakdown of Resummed Perturbation Theory at High Energies
Abstract
Calculations of highenergy processes involving the production of a large number of particles in weaklycoupled quantum field theories have previously signaled the need for novel nonperturbative behavior or even new physical phenomena. In some scenarios, already treelevel computations may enter the regime of largeorder perturbation theory and therefore require a careful investigation. We demonstrate that in scalar quantum field theories with a unique global minimum, where suitably resummed perturbative expansions are expected to capture all relevant physical effects, perturbation theory may still suffer from severe shortcomings in the highenergy regime. As an example, we consider the computation of multiparticle threshold amplitudes of the form $1 \to n$ in $\varphi^6$ theory with a positive mass term, and show that they violate unitarity of the quantum theory for large $n$, even after the resummation of all leading$n$ quantum corrections. We further argue that this is a generic feature of scalar field theories with higherorder selfinteractions beyond $\varphi^4$, thereby rendering the latter unique with respect to its highenergy behavior.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.00549
 Bibcode:
 2021arXiv210900549S
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 27 pages, 3 figures