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

The spin-charge-family theory [1–13], in which spinors, besides the Dirac spin, also carry the second kind of Clifford object—no charges—is a type of Kaluza-Klein theory [14]. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest [1,3,4,10,13,15] in $d=(3+1)$ at low energies all of the properties of quarks and leptons assumed by the standard model. The second kind of spin explains the origin of families. Spinors interact with the vielbeins and the two kinds of spin connection fields, the gauge fields of the two kinds of Clifford objects, which, besides the gravity and known gauge vector fields, manifest in $d=(3+1)$ also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hypercharge ($\mp \frac{1}{2},\pm \frac{1}{2}$, respectively), thereby explaining the origin of the Higgs and 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 color charges, causing transitions of antileptons and antiquarks into quarks and back, thus enabling the appearance and the decay of baryons. These scalar fields show themselves in the presence of the right-handed neutrino condensate, which breaks the $CP$ symmetry, the answer to the question about matter-antimatter asymmetry.

Figure 1

The birth of a right-handed proton out of a positron ${\overline{e}}_L^{+}$, an antiquark ${\overline{u}}_L^{\overline{c2}}$, and a quark (spectator) $u_R^{c2}$. The family quantum number can be any number.

Figure 2

The birth of a left-handed proton out of a positron ${\overline{e}}_R^{+}$, an antiquark ${\overline{u}}_R^{\overline{c2}}$, and a quark (spectator) $u_L^{c2}$. The family quantum number can be any number.