Fermionic states in pure 4D deconstruction

Abstract

We study the structure of fermionic mass eigenstates in a pure four-dimensional deconstruction approach. Unlike the case with the usual higher dimensional deconstruction (or latticized extra dimension), here the doubling of fermionic degrees of freedom is physical, thus there is no need to invoke Wilson terms to eliminate them. The fermionic structure is shaped by two key factors, namely the boundary conditions on fermions and the ratio of two breaking scales involved. The singular value decomposition theorem of linear algebra is employed to shed light into the phenomenologically crucial role of chiral boundary conditions. In this approach, we can explain the "localization" or "delocalization" nature of fermionic zero mode in flavor space and obtain analytically all higher modes. The application of boundary conditions on fermions to the implementation of CKM quark mixing is also found.Comment: 25 pages, discussion expanded, new references added, version to appear in Physical Review

Complete CKM quark mixing via dimensional deconstruction

“…[2,13,15]) usually start out with only Weyl spinors. In the current work, we adopt a different and somewhat more general 4D deconstruction approach [16] where no extra dimension is actually invoked. As a result the fermions to begin with keep a standard 4-component Dirac spinor representation.…”