On a boundary-localized Higgs boson in 5D theories

In the context of a simple five-dimensional (5D) model with bulk matter coupled to a brane-localized Higgs boson, we point out a 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, [Formula: see text] (infinite Kaluza-Klein tower) and [Formula: see text] ([Formula: see text] being the parameter introduced for regularizing the Higgs Dirac peak). This introduces the question of which one is the correct order; we then show that the two possible orders of regularization (called I and II) are experimentally 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 regularizations of type I and II. Beyond a deeper insight into the Higgs peak regularizations, this matching brings another confirmation of the validity of the 5D mixed formalism. 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. The complementary result of the study is that the non-commutativity disappears, both in the 4D and the 5D calculations, in the presence of higher order derivative operators. For clarity, the 4D and 5D analytical calculations, matching with each other, are presented in the first part of the paper, while the second part is devoted to the interpretation of the results.