  We study the renormalization of the nonlinear realization of the SU(2) Higgs
model in the modified minimal subtraction renormalization scheme. We propose
that the effective field method with truncated operator series is trustworthy
even when the Higgs boson is relatively light. Using the technique of
background field method in the coordinate space, we derive the matching
conditions at tree and one loop order, both in the regions where the Higgs
boson is heavy and where it is light. We obtain the complete one-loop anomalous
couplings up to ${\Large O} (p^4)$ in the SU(2) Higgs model. We observe that
the contribution of the gauge bosons and the Goldstone bosons to the anomalous
couplings at the one-loop level is significant. By establishing the
correspondence between our coordinate space calculation and the momentum space
calculation that exists in the literature, we find agreement in all the
matching conditions in the heavy Higgs boson limit.
