The Clockwork Standard Model

TL;DR

This paper explores the linear dilaton background in five dimensions to develop a continuum clockwork model that explains fermion mass hierarchies and mixing, while analyzing KK modes and their collider signatures.

Contribution

It constructs the Clockwork Standard Model in a linear dilaton background, establishing conditions for bulk parameters to address fermion mass hierarchies and flavor structure.

Findings

Bulk field zero modes depend on dilaton couplings and bulk mass parameters.

A sizable expansion parameter allows realistic quark flavor structure without fine-tuning.

KK gauge bosons and gravitons couple differently to fermions, affecting collider phenomenology.

Abstract

We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models. We show that the localization of the zero modes of bulk fields and the mass gap in the KK spectrum depend not only on the bulk dilaton coupling, but also on the bulk mass parameter in the case of a bulk fermion. The consistency from universality and perturbativity of gauge couplings constrain the dilaton couplings to the brane-localized matter fields as well as the bulk gauge bosons. Constructing the Clockwork Standard Model (SM) in the linear dilaton background, we provide the necessary conditions for the bulk mass parameters for explaining the mass hierarchy and mixing for the SM fermions. We can introduce a sizable expansion parameter $\varepsilon=e^{-\frac{2}{3} kz_c}$ for the realistic flavor structure in the quark sector without a fine-tuning in the bulk mass parameters, but at the expense of a large 5D Planck scale. On the other hand, we can use a smaller expansion parameter for lepton masses, in favor of the solution to the hierarchy problem of the Higgs mass parameter. We found that massive Kaluza-Klein (KK) gauge bosons and massive KK gravitons couple more strongly to light and heavy fermions, respectively, so there is a complementarity in the resonance researches for those KK modes at the LHC.