  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 depends 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.
