Abstract
We build rigorously the attractive five-dimensional model where bulk fermions propagate along the $ \mathcal{S}^1 / \mathbb{Z}_2$ orbifold and interact with a Higgs boson localised at a fixed point of the extra dimension. The analytical calculation of the fermion mass spectrum and effective Yukawa couplings is shown to require the introduction of either Essential Boundary Conditions (EBC) imposed by the model definition or certain Bilinear Brane Terms (BBT) in the action, instead of the usual brane-Higgs regularisations. The obtained fermion profiles along the extra dimension turn out to undergo some discontinuities, in particular at the Higgs brane, which can be mathematically consistent if the action is well written with improper integrals. We also show that the $\mathbb{Z}_2$ parity transformations in the bulk do not affect the fermion chiralities, masses and couplings, in contrast with the EBC and BBT, but when extended to the fixed points, they can generate the chiral nature of the theory and even select the Standard Model chirality set-up while fixing as well the fermion masses and couplings. Thanks to the strict analysis developed, the duality with the interval model is scrutinised.
Highlights
We build rigorously the attractive five-dimensional model where bulk fermions propagate along the S1=Z2 orbifold and interact with a Higgs boson localized at a fixed point of the extra dimension
We show that the Z2 parity transformations in the bulk do not affect the fermion chiralities, masses and couplings, in contrast with the essential boundary conditions (EBC) and the bilinear brane terms (BBT), but when extended to the fixed points, they can generate the chiral nature of the theory and even select the Standard Model chirality setup while fixing as well the fermion masses and couplings
As it is well known since the 2000s, the paradigm of models with additional spatial dimensions1 constitutes an attractive alternative to supersymmetry for addressing the Standard Model (SM) puzzle of the gauge hierarchy
Summary
As it is well known since the 2000s, the paradigm of models with additional spatial dimensions constitutes an attractive alternative to supersymmetry for addressing the Standard Model (SM) puzzle of the gauge hierarchy. In particular the decomposition of the action to introduce improper integrals will appear to be required in the presence of orbifold fixed points or pointlike fermion-boson interactions (not located at the boundary of a finite extra space like an interval) Within this new and appropriate approach of the specific points along the extra dimension of the orbifold, we find for the free or Yukawa case that some of the obtained consistent solutions exhibit certain field jumps at these fixed points and localized-interaction point. This interesting result of the possible existence of consistent profile jumps stands against one’s first intuition [43,44], but those jumps are only induced by sign flipping and not by pointlike changes of the absolute value of the wave function amplitudes. The analysis of the present orbifold background with brane-localized fermion-scalar interactions, as well as the previous results [38] on the interval background, show that generally speaking the action expression does not systematically contain all the information allowing to fully define the model: in particular some EBC may be used (in contrast, the BBT are terms in the action) depending on the brane treatment adopted or on the UV completion of the theory (which could introduce the BBT)
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