Rigorous treatment of the $\mathcal{S}^1 / \mathbb{Z}_2$ orbifold model with brane-Higgs couplings

TL;DR

This paper rigorously analyzes a 5D orbifold model with bulk fermions and brane-localized Higgs, clarifying the role of boundary conditions and brane terms in determining fermion spectra and chiral properties.

Contribution

It provides a rigorous formulation of the orbifold model with brane-Higgs interactions, introducing essential boundary conditions and bilinear brane terms for accurate fermion spectrum calculation.

Findings

Fermion profiles can be discontinuous at the Higgs brane.

Bulk Z2 parity does not affect fermion chiralities and couplings.

Extended Z2 symmetry can generate chirality and fix fermion properties.

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.