Mass matrix textures from superstring inspired SO(10) models.

We give a general prescription for deriving quark and lepton mass matrices with “texture” zeros in the framework of superstring inspired SO(10) models. The key to our approach is a new way to naturally implement the doublet–triplet splitting which enables us to obtain symmetric quark and lepton mass matrices which have different structures in the up and the down quark sectors. We illustrate our method by deriving the Georgi–Jarlskog texture which has six predictions in the flavor sector, and then show how it generalizes to other symmetric texture models. Work supported by the Department of Energy Grant #DE-FG02-91ER406267 Work supported by the National Science Foundation Grant #PHY-9119745 One of the major challenges in particle physics today is an understanding of the spectrum of quarks and leptons. In the standard model, all the fermion masses and the mixing angles are arbitrary, accounting for 13 of the 19 free parameters of the theory. This situation is clearly unsatisfactory and has been viewed by many as a hint for physics beyond the standard model. A more fundamental theory, it is hoped, will reduce this arbitrariness, by providing a common origin perhaps for several of these parameters. In the absence of a fundamental theory of fermion masses, it has been popular to assume certain restricted forms for the quark and lepton mass matrices that results in predictions for some of the observables. The hope in this approach is that if the predictions of a particular mass matrix ansatz are borne out by experiments, then a model that leads to a natural derivation of that ansatz may provide the next step in our search for the fundamental theory of nature. The next step beyond the standard model may very well contain a supersymmetric grand unified theory (SUSY GUT). This speculation is supported by the dramatically accurate unification of gauge couplings that has been observed to occur [1] with supersymmetry around the TeV scale following the improved measurements of the low energy couplings at LEP and SLC. Superstring models, which are candidate theories of unifying gravity with the strong and electroweak forces, can lead to a variety of such SUSY GUT groups via an appropriate compactification scheme. It therefore appears to us to be a very desirable program to see if a successful mass matrix ansatz can receive a plausible derivation within a SUSY GUT model inspired by superstrings. This is what we take up in this paper. There are a variety of mass matrix ansatze which can be characterized by their “texture” zeros. For increased predictivity, it is usually assumed that the matrices are symmetric. A well–known example is the Fritzsch ansatz [2] which has a texture similar in form for the up and the down quarks. Such matrices are easily derived from GUTs such as SO(10), which has built–in left–right symmetry and up–down symmetry. If the recent CDF data [3] on the top quark, viz., mt = 174± 17 GeV , holds up, it would appear that the Fritzsch ansatz would be ruled out even after renormalization group corrections are taken into account [4]. Another popular and predictive ansatz is the so–called Georgi–Jarlskog (GJ) texture [5], which assumes symmetric quark and lepton mass matrices, which however, have different forms in the up and down quark sectors. Such matrices, owing to their up–down asymmetry, are less trivial to derive in the context of SUSY GUTs such as SO(10). In this letter, we provide a prescription for deriving such up–down asymmetric matrices in the context of superstring inspired SO(10) models. We will illustrate our method by deriving the GJ texture, which has been the subject of substantial improvement and polishing including renormalization group effects in recent literature [6,7,8,9,10]. We