Can spin-charge-family theory explain baryon number nonconservation?

Abstract

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.