[Paper Review] Aspects of Domain-Wall Standard Model

Nobuchika Okada, Digesh Raut+1 more|arXiv (Cornell University)|Jan 8, 2018

Particle physics theoretical and experimental studies16 references3 citations

TL;DR

This paper proposes the Domain-Wall Standard Model, a 5D field-theory framework where all Standard Model (SM) fields are localized in domain walls within a non-compact fifth dimension, leading to Kaluza-Klein (KK) modes. Using two solvable models with a profile function $ s(y) $, it derives the 4D effective theory, KK-mode spectra, and eigenfunctions, and investigates LHC phenomenology for KK gauge bosons, Higgs boson modifications, and fermion decays into SM particles and Nambu-Goldstone bosons from spontaneous translation symmetry breaking in 5D.

ABSTRACT

We have recently proposed a setup of the "Domain-Wall Standard Model" in a non-compact 5-dimensional space-time, where all the Standard Model (SM) fields are localized in certain domains of the 5th dimension. While the SM is realized as a 4-dimensional effective theory at low energies, the model involves Kaluza-Klein (KK) modes of the SM particles. In this paper we introduce two simple solvable examples which lead to domain-wall configurations for the SM particles and their KK-modes. Based on the examples, we address a variety of phenomenologies of the Domain-Wall SM, such as the KK-mode gauge boson phenomenology at the Large Hadron Collider (LHC), the effect of the KK-mode SM fermions on Higgs boson phenomenology, and the KK-mode fermion search at the LHC with its decay into a corresponding SM fermion and a Nambu-Goldstone boson associated with a spontaneous breaking of the translational invariance in the 5th dimension. We also propose a simple unified picture of localizing all the SM fields.

Motivation & Objective

• To develop a field-theoretical realization of a 5D brane-world model where all SM fields are localized in domain walls in a non-compact fifth dimension.
• To address the phenomenological viability of such a model by constructing explicit, solvable examples of field localization.
• To derive the 4D effective Lagrangian involving KK modes of SM gauge bosons, Higgs, and fermions.
• To explore LHC phenomenology, including KK-mode gauge boson signals, Higgs boson decay modifications, and fermion decay into SM particles and Nambu-Goldstone bosons.
• To propose a unified localization mechanism for all SM fields using a common profile function tied to a kink solution in 5D.

Proposed method

• Introduces a 5D flat Minkowski space with a $ y $-dependent function $ s(y) $ in the gauge kinetic term $ \mathcal{L}_5 = -\frac{1}{4} s(y) F_{MN}F^{MN} $ to localize the U(1) gauge field.
• Solves the KK-mode equation for the gauge field using two explicit profiles: a power-law form and a kink-based form $ s(y) \propto \text{sech}^2(m_\varphi y) $, yielding exact eigenfunctions and mass spectra.
• Applies the same localization mechanism to the Higgs field and its vacuum expectation value (VEV), deriving the 4D effective Higgs sector with KK modes.
• Extends the formalism to SM chiral fermions by introducing a 5D Dirac fermion with a $ y $-dependent mass term, solving for zero-mode and KK-mode wave functions.
• Derives the 4D effective Lagrangian including interactions between SM fields and their KK modes, including couplings to Nambu-Goldstone bosons from spontaneous 5D translation symmetry breaking.
• Proposes a unified localization scheme using $ s(y) = M_G (1 - \frac{\sqrt{\lambda}}{m_\varphi} \varphi_{\text{kink}}(y)^2)^{\gamma_G} $ for gauge, Higgs, and fermion fields, with integer $ \gamma_{G,H} \geq 2 $.

Experimental results

Research questions

• RQ1 How can all SM fields be consistently localized in domain walls within a non-compact 5D space while preserving 4D gauge invariance?
• RQ2 What are the explicit forms of the KK-mode mass spectra and wave functions for gauge bosons, Higgs, and fermions in solvable 5D models?
• RQ3 How do KK modes of SM particles modify Higgs boson phenomenology at the LHC?
• RQ4 What are the signatures for discovering KK-mode fermions at the LHC, particularly decays into a SM fermion and a Nambu-Goldstone boson?
• RQ5 Can a unified localization mechanism for all SM fields be constructed using a single 5D profile function tied to a kink solution?

Key findings

• The model realizes the SM as a 4D effective theory at low energies, with all SM fields localized in domain walls in a non-compact 5D space via a $ y $-dependent function $ s(y) $.
• Two solvable models are constructed: one yielding an infinite tower of KK modes, the other a finite number, both with explicitly calculable eigenfunctions and mass spectra.
• The KK-mode gauge bosons have masses $ m_n \sim n \cdot \Lambda $, where $ \Lambda \lesssim 1 $ TeV, consistent with current LHC constraints on the domain-wall width.
• KK-mode SM fermions induce corrections to Higgs boson couplings, potentially altering branching ratios and production cross sections at the LHC.
• KK-mode fermions can decay into a SM fermion and a Nambu-Goldstone boson from spontaneous 5D translation symmetry breaking, offering a distinctive LHC signature.
• A unified localization scheme is proposed using $ s(y) \propto (1 - \varphi_{\text{kink}}^2)^{\gamma} $, with $ \gamma \geq 2 $, providing a consistent framework for all SM fields and new interactions between KK modes and the 5D scalar field.