An exceptional G(2) extension of the Standard Model from an algebraic conjecture: implications for the strong sector and dark matter

Abstract

A new criterion to extend the Standard Model of particle physics is proposed: the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley-Dickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural and minimal enlargement of the color sector, from a 𝑆𝑈 (3) gauge group to an exceptional Higgs-broken 𝐺 (2) group. In this picture, an additional ensemble of massive 𝐺 (2)-gluons emerges, which is separated from the particle dynamics of the SM and might play the role of dark matter. A fully Lagrangian approach is provided, along with the description of the breaking mechanism, the 𝐺 (2) particle spectrum, the possible composite DM states and their stability examination. Moreover, 𝐺 (2) gauge theory could guarantee peculiar manifestations in astrophysical compact objects, which can be observed in the future studying gravitational waves.