The Clockwork Standard Model

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Springer

Received: June 19, Revised: July 21, Accepted: July 29, Published: September 1,

2020 2020 2020 2020

The Clockwork Standard Model

a

Department of Physics, Chung-Ang University, 84 Heukseok-ro, Seoul 06974, Korea b CERN, Theory Department, 1211 Geneva 23, Switzerland

E-mail: [email protected], [email protected], [email protected] 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 2 sizable expansion parameter ε = e− 3 kzc 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. Keywords: Beyond Standard Model, Field Theories in Higher Dimensions, Classical Theories of Gravity ArXiv ePrint: 2006.03043

c The Authors. Open Access, Article funded by SCOAP3 .

https://doi.org/10.1007/JHEP09(2020)005

JHEP09(2020)005

Yoo-Jin Kang,a Soonbin Kima and Hyun Min Leea,b

Contents 1

2 The clockwork gravity

3

3 Bulk scalars 3.1 Scalar clockwork modes 3.2 Localized couplings of scalar clockwork

5 6 7

4 Bulk fermions 4.1 Fermion clockwork modes 4.2 Localized couplings of fermion clockwork

8 9 11

5 Bulk gauge bosons 5.1 Gauge clockwork modes 5.2 Localized couplings of gauge clockwork 5.3 Bulk couplings of gauge clockwork

12 12 13 14

6 Bulk gravitons 6.1 Graviton clockwork modes 6.2 Localized couplings of graviton clockwork 6.3 Bulk couplings of graviton clockwork

16 16 17 17

7 The 7.1 7.2 7.3 7.4 7.5

18 20 22 24 26 27

Clockwork Standard Model The Yukawa couplings for quarks and leptons The mass hierarchy and mixing for quarks Charged leptons and neutrino masses KK gauge boson couplings KK graviton couplings

8 Conclusions

28

A Matter Lagrangians with dilaton couplings

29

1

Introduction

The Standard Model (SM) of particles physics has been tested well with precision experiments and the consistency of its inner structure has been confirmed with the discovery of the Higgs boson and new data fro