  We perform a systematic one-loop renormalization of a general renormalizable
Yang-Mills theory coupled to scalars and fermions using a regularization scheme
with a smooth momentum cutoff $\Lambda$ (implemented through an exponential
damping factor). We construct the necessary finite counterterms restoring the
BRST invariance of the effective action by analyzing the relevant
Slavnov-Taylor identities. We find the relation between the renormalized
parameters in our scheme and in the conventional $\overline{\rm MS}$ scheme
which allow us to obtain the explicit two-loop renormalization group equations
in our scheme from the known two-loop ones in the $\overline{\rm MS}$ scheme.
We calculate in our scheme the divergences of two-loop vacuum graphs in the
presence of a constant scalar background field which allow us to rederive the
two-loop beta functions for parameters of the scalar potential. We also prove
that consistent application of the proposed regularization leads to
counterterms which, together with the original action, combine to a bare action
expressed in terms of bare parameters. This, together with treating $\Lambda$
as an intrinsic scale of a hypothetical underlying finite theory of all
interactions, offers a possibility of an unconventional solution to the
hierarchy problem if no intermediate scales between the electroweak scale and
the Planck scale exist.
