  Measurements of the Higgs-boson production cross section at the LHC are an
important tool for studying electroweak symmetry breaking at the quantum level,
since the main production mechanism gg-->h is loop-suppressed in the Standard
Model (SM). Higgs production in extra-dimensional extensions of the SM is
sensitive to the Kaluza-Klein (KK) excitations of the quarks, which can be
exchanged as virtual particles in the loop. In the context of the minimal
Randall-Sundrum (RS) model with bulk fields and a brane-localized Higgs sector,
we derive closed analytical expressions for the gluon-gluon fusion process,
finding that the effect of the infinite tower of virtual KK states can be
described in terms of a simple function of the fundamental (5D) Yukawa
matrices. Given a specific RS model, this will allow one to easily constrain
the parameter space, once a Higgs signal has been established. We explain that
discrepancies between existing calculations of Higgs production in RS models
are related to the non-commutativity of two limits: taking the number of KK
states to infinity and removing the regulator on the Higgs-boson profile, which
is required in an intermediate step to make the relevant overlap integrals well
defined. Even though the one-loop gg-->h amplitude is finite in RS scenarios
with a brane-localized Higgs sector, it is important to introduce a consistent
ultraviolet regulator in order to obtain the correct result.
