  We study the non-local regularization for the case of a spontaneously broken
abelian gauge theory in the R_xi gauge with an arbitrary gauge parameter xi. We
consider a simple abelian-Higgs model with chiral couplings as an example. We
show that if we apply the nonlocal regularization procedure [to construct a
nonlocal theory with finite mass parameter ] to the spontaneously broken R_xi
gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we
find that a physical observable in this model, an analogue of the muon
anomalous magnetic moment, evaluated to order O[g^{2}] does indeed show
xi-dependence.We then apply the modified form of nonlocal regularization that
was recently advanced and studied for the unbroken non-abelian gauge theories
and discuss the resulting WT identities and xi-independence of the S-matrix
elements.
