부산대학교 도서관

The spin-charge-family theory predicts before the electroweak break four - rather than the observed three - massless families of quarks and leptons. The 4 x 4 mass matrices of all the family members demonstrate in this theory the same symmetry, which is determined by the scalar fields: the two SU(2) triplets (the gauge fields of the family groups) and the three singlets, the gauge fields of the three charges (Q, Q' and Y') distinguishing among family members. All the scalars have, with respect to the weak and the hyper charge, the quantum numbers of the {\it standard model} scalar Higgs: $\pm \frac{1}{2}$ and $ \mp \frac{1}{2}$, respectively. Respecting by the spin-charge-family theory proposed symmetry of mass matrices and assuming (due to not yet accurate enough experimental data) that the mass matrices are hermitian and real, we fit the six free parameters of each family member mass matrix to the experimental data of twice three measured masses of quarks and to the measured quark mixing matrix elements, within the experimental accuracy. Since any 3 x 3 submatrix of the 4 x 4 unitary matrix determines the whole 4 x 4 matrix uniquely, we are able to predict the properties of the fourth family members provided that the experimental data are enough accurate, which is not yet the case. We, however, found out that the new experimental data for quarks fit better to the required symmetry of mass matrices than the old data and we predict towards which value will more accurately measured matrix elements move. The present accuracy of the experimental data for leptons does not enable us to make sensible predictions.
Comment: 36 pages, 1 figure, updated calculations and comments