Ultraviolet Properties of the Higgs Sector in the Lee-Wick Standard Model

TL;DR

The paper investigates the ultraviolet behavior of the Lee-Wick Standard Model, showing how it cancels quadratic divergences in the Higgs mass and analyzing the renormalization group evolution of the Higgs quartic coupling, revealing a Landau pole at high energies.

Contribution

It provides a detailed analysis of the UV properties of the Lee-Wick Standard Model, including the behavior of the Higgs quartic coupling and the implications for stability and perturbativity.

Findings

Quadratic divergences in Higgs mass cancel due to Lee-Wick fields' dependence on the Higgs background.

The Higgs quartic coupling grows monotonically and hits a Landau pole at a trans-Planckian scale.

Perturbativity and stability bounds on Higgs mass disappear in the Lee-Wick model.

Abstract

The Lee-Wick (LW) Standard Model (SM) offers a new solution to the hierarchy problem. We discuss, using effective potential techniques, its peculiar ultraviolet (UV) behaviour. We show how quadratic divergences in the Higgs mass Mh cancel as a result of the unusual dependence of LW fields on the Higgs background (in a manner reminiscent of Little Higgses). We then extract from the effective potential the renormalization group evolution of the Higgs quartic coupling lambda above the LW scale. After clarifying an apparent discrepancy with previous results for the LW Abelian Higgs model we focus on the LWSM. In contrast with the SM case, for any Mh, lambda grows monotonically and hits a Landau pole at a fixed trans-Planckian scale (never turning negative in the UV). Then, the perturbativity and stability bounds on Mh disappear. We identify a cutoff ~10^{16} GeV for the LWSM due to the hypercharge gauge coupling hitting a Landau pole. Finally, we also discuss briefly the possible impact of the UV properties of the LW models on their behaviour at finite temperature, in particular regarding symmetry nonrestoration.