Quark masses and mixings in E6 x S3:: A Monte Carlo approach

Recently the authors of arXiv:hep-ph/0510321 propose a GUT model for fermion masses and mixings with spontaneously broken S-3 discrete flavor symmetry, where S-3 is the permutation group of three objects. The S-3 breaking pattern in the quark sector is not studied and need further investigation. Since in such a model the number of free parameters is greater than the number of experimental observables, an analytical fit of all the parameters is impossible. To go forward with the model building and to deal with this problem we have used a statistical analysis. We have found that S-3 is totally broken and the up-type quarks matrix is approximatively diagonal while down-type quarks matrix is not symmetric and it is parametrized by three couplings, g(d), g(L)(d) and g(3)(d). It has been found that g(L)(d) is slightly smaller than g(d) = 1 and it is of order one, while g(3)(d) similar to lambda(3) where lambda is the Cabibbo angle. An analytical study of the dependence of V-cb and V-ub from the coupling g(L)(d) and g(3)(d) is also presented.