Dynamical generation of fermion mass hierarchy in an extra dimension

We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a single generation of fermions. A five-dimensional gauge theory on an interval with point interactions (zero-width brans) 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.