The Lee-Wick (LW) standard model (SM) offers a new solution to the hierarchy problem. We discuss, using effective potential techniques, its peculiar UV behavior. We show how quadratic divergences in the Higgs mass $M_h$ 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 $M_h$, $\lambda$ 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 $M_h$ disappear. We identify a cutoff $\sim {10}^{16}\mathrm{GeV}$ 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 behavior at finite temperature, in particular, regarding symmetry nonrestoration.

• Received 8 February 2011

DOI:https://doi.org/10.1103/PhysRevD.83.075019