Dihedral Flavor Symmetry from Dimensional Deconstruction.pdf

a r X i v : h e p - p h / 0 5 0 6 0 4 3 v 1 6 J u n 2 0 0 5 KANAZAWA-05-07 To my late father Dihedral Flavor Symmetry from Dimensional Deconstruction Jisuke Kubo Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan Abstract Extra dimension deconstructed on a closed chain has naturally the symmetry of a regular poly- gon, the dihedral symmetry DN . We assume that the fields are irreducible representations of the binary dihedral group Q2N , which is the covering group of DN . It is found that although the orbifold boundary conditions break the dihedral invariance explicitly, the Q2N symmetry appears as an intact internal, global flavor symmetry at low energies. A concrete predictive model based on Q6N with an odd N is given. PACS numbers: 11.25.Mj,11.30.Hv, 12.15.Ff, 14.60.Pq, 02.20.Df 1 I. INTRODUCTION The Yukawa sector of the standard model (SM) contains a large number of redundant parameters. The presence of the redundant parameters is not related to a symmetry in the SM. That is, they will appear in higher orders in perturbation theory even if they are set equal to zero at the level. These redundant parameters may become physical parameters when going beyond the SM, and, moreover, they can induce flavor changing neutral currents (FCNCs) and CP violating phenomena that are absent or strongly suppressed in the SM. One of the most well known examples is the case of the minimal supersymmetric model (MSSM). Since the SM can not control the redundant parameters, the size of the new FCNCs and CP violating phases may be unacceptably large unless there is some symmetry, or one fine tunes their values 1. A natural guidance to constrain the Yukawa sector and to reduce the redundancy of this sector is a flavor symmetry. It has been recently realized that nonabelian discrete flavor symmetries, especially dihedral symmetries, can not only reduce the redundancy, but also partly explain the large mixing of neutrinos 2. When supersymmetrized, it ha