A $\mathrm{U}(2) \times \mathrm{U}(3)$ gauge theory extension of the standard model

Abstract: We consider an extension of the standard model based on the group $\mathrm{U}(2) \times \mathrm{U}(3)$, which is naturally compatible with the standard model interacting-particle representations and the spontaneous symmetry breaking of $\mathrm{U}(2) \times \mathrm{U}(3)$ to an electrostrong $\mathrm{U}(3)$. In its minimal version, the model only adds one extra $\mathrm{U}(1)$ gauge boson and it implies that the hypercharge is distributed between the factors of the hyperweak and hyperstrong forces. We show that the anomaly cancellation condition can be solved by adding exotic fermions associated with a $16$-dimensional representation of $\mathrm{U}(2) \times \mathrm{U}(3)$. A brief discussion of the mechanism of the spontaneous breakdown of $\mathrm{U}(2) \times \mathrm{U}(3)$ in the gauge boson sector is given.