  We study the allowed parameter space of the scalar sector in the superweak
extension of the standard model (SM). The allowed region is defined by the
conditions of (i) stability of the vacuum and (ii) perturbativity up to the
Planck scale, (iii) the pole mass of the Higgs boson falls into its
experimentally measured range. We employ renormalization group equations and
quantum corrections at two-loop accuracy. We study the dependence on the Yukawa
couplings of the sterile neutrinos at selected values. We also check the
exclusion limit set by the precise measurement of the mass of the W boson. Our
method for constraining the parameter space using two-loop predictions can also
be applied to simpler models such as the singlet scalar extension of the SM in
a straightforward way.
