The Breakdown of Resummed Perturbation Theory at High Energies

TL;DR

This paper reveals that resummed perturbation theory in scalar quantum field theories can break down at high energies, leading to unitarity violations in multiparticle production amplitudes, especially beyond $\

Contribution

It demonstrates the limitations of resummed perturbation theory in scalar theories with higher-order interactions at high energies, highlighting potential unitarity issues.

Findings

Resummed perturbation theory may fail at high energies in scalar theories.

Multiparticle amplitudes can violate unitarity for large particle numbers.

Higher-order scalar interactions beyond $\

Abstract

Calculations of high-energy processes involving the production of a large number of particles in weakly-coupled quantum field theories have previously signaled the need for novel non-perturbative behavior or even new physical phenomena. In some scenarios, already tree-level computations may enter the regime of large-order 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 high-energy 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 may 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 higher-order self-interactions beyond $\varphi^4$, thereby rendering the latter unique with respect to its high-energy behavior.