High scale boundary conditions with an additional complex singlet

TL;DR

This paper explores how adding a complex scalar to the Standard Model allows for Planck scale boundary conditions on Higgs interactions, compatible with current measurements, but necessitating lighter scalars below 600 GeV.

Contribution

It demonstrates that the boundary condition $ ext{lambda}=eta_ ext{lambda}=0$ at the Planck scale is feasible with an extra complex scalar, extending previous analyses.

Findings

Boundary condition $ ext{lambda}=eta_ ext{lambda}=0$ is compatible with current data.

Additional scalars lighter than about 600 GeV are required.

Two-loop renormalisation group running was used for analysis.

Abstract

We investigate Planck scale boundary conditions on Higgs quartic interactions and their $\beta$-functions in the SM augmented by an additional complex scalar. We use renormalisation group running at two-loops, and include both theoretical and experimental constraints. We find that the boundary condition $\lambda=\beta_\lambda=0$ at the Planck scale is compatible with the current Higgs and top mass measurements, but requires additional scalars lighter than about $600\,$GeV.