Is There Physics in Landau Poles ?

TL;DR

This paper introduces a solvable quantum mechanics model to analyze Landau poles, showing they are artifacts of perturbation theory and do not indicate new physics at 1 TeV, challenging common assumptions.

Contribution

A new exactly solvable model of singular quantum mechanics demonstrating that Landau poles are artifacts of perturbation theory rather than physical phenomena.

Findings

Landau poles do not appear in exact observables

Landau poles arise only in truncated perturbation theory with incorrect sign coupling

Implications suggest no new physics at 1 TeV based on Landau pole arguments

Abstract

Triviality and Landau poles are often greeted as harbingers of new physics at 1 TeV. After briefly reviewing the ideas behind this, a model of singular quantum mechanics is introduced. Its ultraviolet structure, as well as some features of its vacuum, related to triviality, very much parallel $\lambda\phi^4$. The model is solvable, exactly and perturbatively, in any dimension. From its analysis we learn that Landau poles do not appear in any exactly computed observable, but only in truncated perturbation theory, when perturbation theory is performed with the wrong sign coupling. If these findings apply to the standard model no new physics at 1 TeV should be expected but only challenges for theorists.