  In the context of warped extra-dimensional models which address both the
Planck-weak- and flavor-hierarchies of the Standard Model (SM), it has been
argued that certain observables can be calculated within the 5D effective field
theory only with the Higgs field propagating in the bulk of the extra
dimension, just like other SM fields. The related studies also suggested an
interesting form of decoupling of the heavy Kaluza-Klein (KK) fermion states in
the warped 5D SM in the limit where the profile of the SM Higgs approaches the
IR brane. We demonstrate that a similar phenomenon occurs when we include the
mandatory KK excitations of the SM Higgs in loop diagrams giving dipole
operators for SM fermions, where the earlier work only considered the SM Higgs
(zero mode). In particular, in the limit of a quasi IR-localized SM Higgs, the
effect from summing over KK Higgs modes is unsuppressed (yet finite), in
contrast to the naive expectation that KK Higgs modes decouple as their masses
become large. In this case, a wide range of KK Higgs modes have
quasi-degenerate masses and enhanced couplings to fermions relative to those of
the SM Higgs, which contribute to the above remarkable result. In addition, we
find that the total contribution from KK Higgs modes in general can be
comparable to that from the SM Higgs alone. It is also interesting that KK
Higgs couplings to KK fermions of the same chirality as the corresponding SM
modes have an unsuppressed overall contribution, in contrast to the result from
the earlier studies involving the SM Higgs. Our studies suggest that KK Higgs
bosons are generally an indispensable part of the warped 5D SM, and their
phenomenology such as signals at the LHC are worth further investigation.
