  We construct asymptotically free renormalization group trajectories for the
generic nonabelian Higgs model in four-dimensional spacetime. These
ultraviolet-complete trajectories become visible by generalizing the
renormalization/boundary conditions in the definition of the correlation
functions of the theory. Though they are accessible in a controlled
weak-coupling analysis, these trajectories originate from threshold phenomena
which are missed in a conventional perturbative analysis relying on the deep
Euclidean region. We identify a candidate three-parameter family of
renormalization group trajectories interconnecting the asymptotically free
ultraviolet regime with a Higgs phase in the low-energy limit. We provide
estimates of their low-energy properties in the light of a possible application
to the standard model Higgs sector. Finally, we find a two-parameter subclass
of asymptotically free Coleman-Weinberg-type trajectories that do not suffer
from a naturalness problem.
