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.
Highlights
The Standard Model (SM) is an enormously successful description of the strong and electroweak interactions, and the discovery of the Higgs at the LHC [1] is just one in a long list of experimental validations that it can boast
We investigate the phenomenologically viable regions of parameter space in the complex singlet extension of the SM to examine the effect of high-scale boundary conditions
We find ourselves in the dark matter (DM) phase, where mixing is allowed only between h and the real part of the complex singlet field s1
Summary
The Standard Model (SM) is an enormously successful description of the strong and electroweak interactions, and the discovery of the Higgs at the LHC [1] is just one in a long list of experimental validations that it can boast. Supersymmetric or composite Higgs models can provide a 125 GeV Higgs, but in general this requires either a large tuning of parameters or a nonminimal field content [3,4,5], leaving us in a situation where they are neither favored nor excluded Add to this the seemingly very SM-like nature of the Higgs [2,6,7,8] and we find searches for BSM physics in a difficult position. These properties of the Higgs quartic coupling have led to investigations into whether they are boundary conditions that are a consequence of some high-scale dynamics at MPl [14,15,16,17,18,19,20].
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