Construction of anSO(10)×U(1)Fmodel of the Yukawa interactions

Abstract

We construct a supersymmetric SO(10)×U (1) F model of the Yukawa interactions at the grand unification scale from knowledge of a phenomenological set of mass matrices obtained by a previous bottom-up approach. The U (1) F family symmetry determines the textures for the Majorana and generic Dirac mass matrices, while the SO(10) symmetry relates each particular element of the up, down, neutrino and charged lepton Dirac matrices. The dominant second and third family contributions in the Dirac sector are renormalizable, while the remaining contributions to the Dirac mass matrices are of higher order, restricted by the U (1) F family symmetry to a small set of tree diagrams, and mainly complex-symmetric. The tree diagrams for the Majorana mass matrix are all non-renormalizable and of progressively higher-order, leading to a nearly * Permanent address † Electronic address: ALBRIGHT@FNALV ‡ Electronic address: PHYSSNA@OSUCC I. INTRODUCTIONThe standard model (SM) of strong and electroweak interactions, while providing excellent agreement with experiment todate, is known to be woefully inadequate to explain the mass spectrum and mixings of the three families of quarks and leptons. One needs to go beyond the standard model in order to relate the independent Yukawa couplings to each other.Of the various possibilities, supersymmetric grand unified theories and superstring theories seem to hold the most promise for successfully incorporating the Yukawa interactions in a more satisfactory fashion. In this paper we shall restrict our attention to supersymmetric SO(10) grand unification, which has been shown [1] to unify the gauge couplings successfully at a scale of Λ SGU T ∼ 10 16 GeV.It is a generally held opinion that knowledge of the mass matrices in the weak flavor basis can provide insights into the dynamical mass-generating mechanism.[2] This follows from the fact that the mass eigenvalues are obtained by diagonalization of the mass matrices, while the mixing matrices in the mass eigenbasis can be constructed from knowledge of the diagonalizing matrices connecting the two bases. By starting from the correct mass matrices, one should then be able to deduce the observed quark and lepton masses and mixings after evolving the results down to the present "low energy" scales.Generally two procedures are at one's disposal for the identification of the "correct" mass matrices. One can attempt to postulate a particular structure or "texture" for the mass matrices based on some well-defined and presumably simple theoretical concepts such as the unification group and/or the number of texture zeros present.[3] This procedure has been employed by most researchers in the past twenty years. Alternatively, one can make use of the known low energy mass and mixing data, supplemented by reasonable guesses for data which is not yet well determined, in order to extract mass matrices within some framework at the unification scale which yield the low energy data in question. Of special -3-FERMILAB-Pub-95/236-T interest are neutrino s...

A non-minimal ${\rm SO}(10) \times{\rm U}(1)_{\rm F}$ SUSY - GUT model obtained from a bottom-up approach

“…With twelve input parameters in the form of Yukawa couplings times VEV's, the numerical results obtained for the 3 heavy Majorana masses and 20 low energy parameters for the quark and lepton masses and two mixing matrices were found to be in exceptionally good agreement with the low energy data in the neutrino scenario in question as shown in [2].…”

“…In a recent series of papers [1,2], the author in collaboration with S. Nandi began a program to construct a viable model for the fermion quark and lepton masses and mixings at the supersymmetric grand unification scale. The program envisaged by us has evolved in three stages, beginning with a bottom-up approach which ensures accurate results for the known low-energy data without introducing an undue amount of theoretical bias at the outset.…”

“…In the second stage [2] of our program, we attempted to find a model incorporating a family symmetry which yields the above matrices determined phenomenologically from our bottom-up approach. Success was obtained by introducing a global U(1) F family symmetry [19] which uniquely labels each one of the three light families, as well as conjugate pairs of heavy families and various Higgs representations.…”

Neutrino masses and mixing with non-anomalous abelian flavor symmetries

“…If supersymmetry is not to be broken at the scale of spontaneous H-breaking, then H should be broken along a D-flat direction. The simplest possibility then is that two scalars, S and S, of opposite H-charges (say, ±1) assume equal VEVs, S = S [42][43][44][45][46][47][48]13].…”

“…In addition to supersymmetry and to the Standard Model gauge symmetry, there is an approximate U (1) H symmetry that is broken by two small parameters λ and λ [49,[42][43][44][45][46][47][48]13]. The two parameters are assumed to be equal in magnitude:…”