Numerical analysis of SO(10) models with flavour symmetries

Abstract

We consider a supersymmetric SO(10) Grand Unified Theory (GUT) in which the fermion masses are generated by renormalizable Yukawa couplings. Consequently, the scalar multiplets under consideration belong to the irreps 10, 126 and 120 of SO(10). We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases pertain to one-generator Abelian groups and only one case has a two-generator symmetry group. Supersymmetry enters through the numerical examination of those cases, in which we have used the charged-fermion masses evaluated at the GUT scale through renormalization-group running in the context of the Minimal Supersymmetric Standard Model. However, the numerical analysis rules out almost all the cases, leaving only few viable ones which are compatible with the data on the fermion masses and mixings. In order to test the viability of each case, and to find adequate numerical values for its parameters, we construct a minimization function chi^2 which relate experimental data with the observables (masses and mixing parameters) to be fitted. For the numerical minimization we have employed the Differential Evolution algorithm. By modifying errors in the chi^2 function and diversely restricting parameters space we have thus been able to test, for each case, more local minima, and to find the minima closer to the global minimum.