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 ε = {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.
Highlights
We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models
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 introduced various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions, and showed the bulk profile of the zero mode as well as the KK spectrum in each case
Summary
We first review the warped geometry with the linear dilaton background in five dimensions. The extra dimension is bounded to z ∈ The linear dilaton background differs from the warped extra dimension without a dilaton [53], because the 5D Planck scale can be taken to a small value due to the exponentially large proper length of the extra dimension in the former case. In the linear dilaton background, it is remarkable that M5 and k < M5 can be much smaller than the Planck scale, addressing the hierarchy problem with the warped extra dimension and allowing for the KK masses of order k as will be discussed in the later sections. 0.12, which is appropriately sizable for obtaining the realistic quark Yukawa couplings from the bulk fermions in the later discussion
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