We propose a new model which can simultaneously and naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo-Kobayashi-Maskawa matrix from the geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermions at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of the nondiagonal elements of fermion mass matrices is found to be severely restricted due to the geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy. a Recently, the ATLAS and CMS experimental groups of the CERN Large Hadron Collider (LHC) have announced the excess at 125 GeV, which is consistent with the Standard Model (SM) Higgs boson, with a local significance of 5σ after combining 7 TeV and 8 TeV data [1,2]. This amazing happening means that the mysteries behind the last missing piece of the SM are ready to be unveiled. But the SM still has many points which are unclear, in spite of lots of effort from physicists.One is called the "quark mass hierarchy problem". In the SM, we are forced to comply with a hierarchy of almost five orders of magnitude in Yukawa couplings of quarks for describing the suitable quark masses. Closely related to this issue, the SM cannot answer the mechanism behind the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes the strengths of generationchanging interactions in the SM. In addition to these two issues, we cannot explain why we introduce three copies of quarks whose quantum numbers are the same except for their masses and the degrees of mixings in the above interactions. Many attempts have been made to explain the issues within the four-dimensional (4D) Quantum Field Theory (QFT) framework with, including, for example, launching new continuous and/or discrete symmetries, introducing new matter and interactions, and discussing renormalization group (RG) effects from a theory at a (very) high energy scale compared to the electroweak (EW) scale.When we focus on the case in five dimensions (5D), where there is one additional spatial direction, we can find a new useful tool for tackling the above and other problems: geometry. Two of the most renowned studies which show the power of geometry are [3,4], where the authors proposed innovative ways for solving the hierarchy problem. Extra space can have a huge variety of structure, which are detected as differences from the 4D effective theory point of view. In a 5D QFT framework, we also find new mechanisms which we cannot find in 4D, for example, generating spontaneous gauge symmetry breaking with a global Wilson loop operator [5][6][7], and symmetry br...
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N = 2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N = 2 supercharges. Spontaneous supersymmetry breaking due to point interactions and an extension to higher N-extended supersymmetry are also discussed.
We show that a quantum-mechanical N = 2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N = 2 supercharges are explicitly constructed in terms of differential forms. The analysis can be extended to extra dimensions with boundaries, and for a single extra dimension we clarify a possible set of boundary conditions consistent with 5d gauge invariance, although some of the boundary conditions break 4d gauge symmetries.
We discuss gauge symmetry breaking in a general framework of gauge theories on an interval. We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements. It is shown that with these boundary conditions the scalar field can acquire a nontrivial vacuum expectation value even if the scalar mass square is positive. Any nonvanishing vacuum expectation value cannot be a constant but, in general, depends on the extra dimensional coordinate of the interval. 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. We also discuss 4d chiral fermions and fermion mass hierarchies in our gauge symmetry breaking scenario.Comment: 16 pages, 8 figure
We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N = 2n supercharges are explicitly constructed and a class of point singularities compatible with supersymmetry is clarified. Key ingredients in our construction are n sets of discrete transformations, each of which forms an su(2) algebra of spin 1/2. The degeneracy of the spectrum and spontaneous supersymmetry breaking are briefly discussed.
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