Note on scattering in asymptotically nonlocal theories

TL;DR

This paper explores how scattering processes in asymptotically nonlocal quantum field theories reveal nonlocal effects at high energies, even when Lee-Wick resonances are decoupled, impacting observable phenomena related to the hierarchy problem.

Contribution

It analyzes the energy dependence of scattering cross sections in asymptotically nonlocal theories, highlighting how nonlocality manifests beyond Lee-Wick resonance scales.

Findings

Scattering amplitudes reflect emergent nonlocality at high energies.

Decoupled Lee-Wick resonances do not eliminate nonlocal effects.

Observable consequences arise in hierarchy problem solutions.

Abstract

It is possible to formulate theories with many Lee-Wick particles such that a limit exists where the low-energy theory approaches the form of a ghost-free nonlocal theory. Such asymptotically nonlocal quantum field theories have a derived regulator scale that is hierarchically smaller than the lightest Lee-Wick resonance; this has been studied previously in the case of asymptotically nonlocal scalar theories, Abelian and non-Abelian gauge theories, and linearized gravity. Here we consider the dependence on center-of-mass energy of scattering cross sections in these theories. While Lee-Wick resonances can be decoupled from the low-energy theory, scattering amplitudes nonetheless reflect the emergent nonlocality at the scale where the quadratic divergences are regulated. This implies observable consequences in theories designed to address the hierarchy problem, even when the Lee-Wick resonances are not directly accessible.