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.
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