High scale boundary conditions with an additional complex singlet

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.

23 pages, 13 figures; version accepted for publication

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