Can we predict the fourth family masses for quarks and leptons?

Abstract

In the spin-charge-family theory four massless families of quarks and leptons before the electroweak break are predicted. Mass matrices of all the family members demonstrate in this proposal the same symmetry, determined by the family groups. There are scalar fields - two $SU(2)$ triplets, the gauge fields of the family quantum numbers, and three singlets, the gauge fields of the three charges ( $Q,Q^{\prime }$ and $Y^{\prime }$)- all doublets with respect to the weak charge, which determine mass matrices on the tree level and, together with other contributions, also beyond the tree level. The symmetry of mass matrices remains unchanged for all loop corrections. The three singlets are, in loop corrections also together with other contributors, responsible for the differences in properties of the family members. Taking into account by the spin-charge-family theory proposed symmetry of mass matrices for all the family members and simplifying study by assuming that mass matrices are Hermitian and real and mixing matrices real, we fit free parameters of mass matrices to experimental data within the experimental accuracy. Calculations are in progress.

23 pages, new title, substantially revised, to appear in the Proceedings to the 16th Bled Workshop "What Comes Beyond Standard Models", DMFA ZALOZNISTVO, December 2013, Vol. 14, No. 2

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