Higgs mechanism and flavor structure from an extra dimension

In this dissertation, we clarify the Higgs mechanism and the flavor structure of the fermions from a viewpoint of higher dimensional gauge theories with focusing on effects of boundary conditions. First of all, we derive a general class of possible boundary conditions for a complex scalar field in the context of five-dimensional gauge theories on an interval. It is shown that general boundary conditions for the scalar field, which are compatible with several consis- tency requirements, are characterized by two parameters. Those boundary conditions are wider than the boundary conditions commonly used and are known as the Robin boundary condition. With the Robin boundary condition the scalar field can acquire a nonvanishing vacuum expectation value even if the scalar mass square is positive. We need a negative mass square to the gauge symmetry breaking in usual Higgs mechanism. Furthermore, the vacuum expectation value of the scalar turns out to inevitably depend on the extra dimen- sional coordinate of the interval and is given in terms of Jacobi elliptic functions. The phase diagram of broken/unbroken gauge symmetry possesses a rich structure in the parameter space of the length of the interval, the scalar mass and the boundary conditions. Secondly, we derive a general class of possible boundary conditions for a fermion in the context of five-dimensional gauge theories on an interval. It is shown that general boundary conditions for a fermion are given by the Dirichlet boundary condition. Under the Dirichlet boundary condition, a four-dimensional chiral fermion zero mode appears in the low energy effective theory. Furthermore, we can introduce additional boundary points on the bulk without any inconsistency in the fermion case. The Dirichlet boundary condition for the fermion at additional boundary points does not contradict the consistency requirements, e.g. five-dimensional gauge invariance, unlike the scalar case. In the situation, profiles of chiral fermion zero modes are split and localized, and we can realize three generations from a single five-dimensional fermion. An extra dimensional coordinate-dependent vacuum expectation value of a scalar, which might be produced by the Robin boundary condition, is useful to explain the fermion mass hierarchy in this framework. As an application we construct a phenomenological model which can naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo-Kobayashi-Maskawa matrix from the geometry of an extra dimension. We also discuss a vacuum expectation value of the Higgs doublet under the twisted boundary condition. To solve the fermion generation problem, one might consider a single generation model with a source of generations. In that case, a model does not contain a CP phase degree of freedom as our phenomenological model. Under the twisted boundary condition, the vacuum expectation value of the Higgs doublet possesses a nontrivial extra dimensional coordinate-dependent phase. Through the overlap integrals, localized fermion zero modes pick up different phases to their masses from the extra dimensional coordinate- dependent vacuum expectation value of the Higgs. Thus the phase of the Higgs’s vacuum expectation value can be a new source of the CP phase in the context of higher dimensional gauge theories. We apply this mechanism to our phenomenological model to fix the absent of CP phase which appears in Cabibbo-Kobayashi-Maskawa matrix.