The attractive class of higher-dimensional scenarios, based on a brane-localised Higgs boson coupled to bulk fermions, can address both the puzzle of the structure of the flavour space and the gauge hierarchy problem. In this framework, a key question arises due to the possibility of fermion wave function discontinuities at the Higgs boundary: how to build rigorously the Lagrangian and calculate the fermion mass spectrum as well as the effective four-dimensional (4D) Yukawa couplings? We show that the proper treatment, leading to physically consistent solutions, does not rely on any Higgs peak regularisation but requires the presence of certain bilinear brane terms. In particular, no profile jump should appear and the Higgs regularisations turn out to suffer from mathematical discrepancies reflected in two non-commutativities of calculation steps debated in the literature. The introduction of bilinear brane terms can alternatively by replaced by vanishing conditions for probability currents at the considered flat interval boundaries. Indeed, both contribute to the definition of the field geometrical configuration of the model, even in the free case. The bilinear brane terms could allow to elaborate an ultra-violet origin of the chiral nature of the Standard Model and of its chirality distribution among quarks/leptons. The current conditions are implemented through essential boundary conditions to be contrasted with the natural boundary conditions derived from the action variation. All these theoretical conclusions are confirmed in particular by the converging exact results of the 4D versus 5D approaches. The analysis is completed by a description of the appropriate energy cut-off procedure in the present context. The new calculation methods presented, implying the independence of excited fermion masses and 4D Yukawa couplings on the 'wrong-chirality' Yukawa terms, have impacts on phenomenological results like the relaxing of previously obtained strong bounds on Kaluza-Klein masses induced by flavour changing reactions generated via tree-level exchanges of the Higgs field.

In this paper, we propose to compactify a single Large Extra Dimension (LED) on a star/rose graph with a large number of identical leaves/petals. The 5D Planck scale can be chosen to be [Formula: see text] TeV which can provide a path to solve the gauge hierarchy problem. The leaf/petal length scale is of [Formula: see text], where [Formula: see text] GeV is the weak scale, without the large geometrical hierarchy of the traditional LED models to stabilize. The 4D fields of the SM are localized on a 3-brane at the central vertex of the star/rose graph. We predict a tower of feebly coupled weak scale Kaluza–Klein (KK) gravitons below a regime of strongly coupled gravitational phenomena above the TeV scale. Moreover, we reformulate in our setup the LED mechanism to generate light Dirac neutrinos, where the right-handed neutrinos are KK-modes of gauge singlet fermions propagating in the bulk. A large number of KK-gravitons and KK-neutrinos interact only gravitationally and thus constitute a hidden sector.