In the context of a simple five-dimensional (5D) model with bulk matter coupled to a brane-localized Higgs boson, we point out a new non-commutativity in the 4D calculation of the mass spectrum for excited fermion towers: the obtained expression depe
nds on the choice in ordering the limits, N->infinity (infinite Kaluza-Klein tower) and epsilon->0 (epsilon being the parameter introduced for regularizing the Higgs Dirac peak). This introduces the physical question of which one is the correct order; we then show that the two possible orders of regularization (called I and II) are physically equivalent, as both can typically reproduce the measured observables, but that the one with less degrees of freedom (I) could be uniquely excluded by future experimental constraints. This conclusion is based on the exact matching between the 4D and 5D analytical calculations of the mass spectrum - via the regularizations of type I and II. Beyond a deeper insight into the Higgs peak regularizations, this matching also allows us to confirm the validity of the usual 5D mixed-formalism and to clarify the UV cut-off procedure. All the conclusions, deduced from regularizing the Higgs peak through a brane shift or a smoothed square profile, are expected to remain similar in realistic models with a warped extra-dimension.
