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Abstract
We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a singlet generation of fermions. A five dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra-dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the point interactions control the magnitude of the fermion mass hierarchy and are determined by the minimization condition of the Casimir energy. As a result of the minimization of the Casimir energy, an exponential mass hierarchy appears dynamically. We also discuss the stability of the extra dimension.
Highlights
The standard model (SM), which provides an articulate description of the nature around TeV energy scale, was completed by the discovery of the Higgs boson [1,2]
We further show that the scalar field can possess a coordinate-dependent vacuum expectation value (VEV) on the extra dimension [25,26,27,28,38,39,40], 3See [35] ( [36,37]) for generating Yukawa hierarchies through multiple dynamical scales
We proposed a new mechanism to produce a fermion mass hierarchy dynamically by introducing the point interactions to the 5d gauge theory on an interval
Summary
The standard model (SM), which provides an articulate description of the nature around TeV energy scale, was completed by the discovery of the Higgs boson [1,2]. One possibility in the context of four-dimensional (4d) gauge theory is a scenario with noncompact gauge symmetry, which can naturally produce the fermion mass hierarchy and three generations [4,5,6,7,8] Another way is achieved by using extra dimensions. The minimization of the Casimir energy determines the positions of the point interactions, which are important parameters to produce the fermion mass hierarchy, and leads to the stability of the extra dimension. Which is found to be a crucial ingredient of our dynamical generation mechanism for generating a fermion mass hierarchy
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