Abstract
The class of higher-dimensional scenarios, based on a brane-localised Higgs boson coupled to bulk fermions, can address both the flavour puzzle and gauge hierarchy problem. A key question arises due to the possibility of fermion profile discontinuities at the Higgs boundary: how to calculate rigorously the fermion mass spectrum and 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 (BBT). 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 BBT can by replaced by vanishing conditions for probability currents at the considered flat interval boundaries. Both contribute to the definition of the field geometrical configuration of the model, even in the free case. The BBT 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 via 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. 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 through exchanges of the Higgs field.
Highlights
The paradigm of scenarios with extra spatial dimensions represents an alternative to supersymmetry for addressing the deep gauge hierarchy problem of the Standard Model (SM)
We show that the proper treatment, leading to physically consistent solutions, does not rely on any Higgs peak regularization but requires the presence of certain bilinear brane terms
At a brane without Yukawa coupling, instead of including such a bilinear term, we find that one can alternatively impose as an essential boundary condition the condition of a fermion current along the extra dimension vanishing at this brane—and exclusively within the 4D approach in case of a brane with localized Yukawa interaction
Summary
The paradigm of scenarios with extra spatial dimensions (and the composite Higgs models dual via the AdS=CFT correspondence) represents an alternative to supersymmetry for addressing the deep gauge hierarchy problem of the Standard Model (SM). The rigorous results obtained for the KK mass spectrum and effective 4D Yukawa couplings are different from the ones derived in general through the Higgs peak regularization, as it is detailed in the present paper This difference is physical, affecting phenomenological studies on indirect searches of KK states at high-energy colliders. The correct mass spectrum obtained here allows us to point out the necessity, for bulk fermions (with or without coupling to a brane-localized scalar field), to have certain bilinear brane terms at boundaries which are fermion mass terms from the point of view of the spinorial structure but do not introduce new mass parameters.3 Such terms guarantee the existence of physical solutions (with correct profile normalizations and Hermitian conjugate boundary conditions and satisfying the decoupling limit argument) derived via the least action principle through the variation calculus.
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