Masses and Mixing Matrices of Families of Quarks and Leptons Within the Spin-Charge-Family theory, predictions beyond the tree level

TL;DR

This paper analyzes one-loop quantum corrections to fermion masses and mixing matrices in a theory unifying spin and charges, aiming to explain differences between quark and lepton properties beyond the tree level.

Contribution

It provides a detailed analysis of one-loop corrections to fermion masses and mixing matrices within the spin-charge-family theory, extending understanding beyond tree-level predictions.

Findings

Loop corrections involve gauge bosons and scalar fields.

Mass matrices for quarks and leptons are correlated at tree level.

Beyond tree level, corrections may explain mass and mixing differences.

Abstract

The {\it theory unifying spin and charges and predicting families}, proposed by N.S.M.B., predicts at the low energy regime two (in the mixing matrix elements decoupled) groups of four families. There are two kinds of contributions to mass matrices in this theory. One kind distinguishes on the tree level only among the members of one family, that is among the $u$-quark, $d$-quark, neutrino and electron, the left and right handed, while the other kind distinguishes only among the families. Mass matrices for $d$-quarks and electrons are on the tree level correspondingly strongly correlated and so are mass matrices for $u$-quarks and neutrinos, up to the term, the Majorana term, which is nonzero only for right handed neutrinos. Beyond the tree level both kinds of contributions start to contribute coherently and it is expected that a detailed study of properties of mass matrices beyond the tree level explains drastic differences in masses and mixing matrices between quarks and leptons. We report in this paper on analysis of one loop corrections to the tree level fermion masses and mixing matrices. Loop diagrams are mediated by the gauge bosons and the two kinds of scalar fields. A detailed numerical analysis of fermion masses and mixing, including neutrinos, within this scenario is in progress and preparation.