Flatland: abelian extensions of the Standard Model with semi-simple completions

Abstract We parametrise the space of all possible flavour non-universal u $$ \mathfrak{u} $$ (1) X extensions of the Standard Model that embed inside anomaly-free semi-simple gauge theories, including up to three right-handed neutrinos. More generally, we parametrise all abelian extensions (i.e. by any number of u $$ \mathfrak{u} $$ (1)’s) of the SM with such semi-simple completions. The resulting space of abelian extensions is a collection of planes of dimensions ≤ 6. Numerically, we find that roughly 2.5% of anomaly-free u $$ \mathfrak{u} $$ (1) X extensions of the SM with a maximum charge ratio of ±10 can be embedded in such semi-simple gauge theories. Any vector-like anomaly-free abelian extension embeds (at least) inside g $$ \mathfrak{g} $$ = su $$ \mathfrak{su} $$ (12) ⊕ su $$ \mathfrak{su} $$ (2) L ⊕ su $$ \mathfrak{su} $$ (2) R. We also provide a simple computer program that tests whether a given u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕... charge assignment has a semi-simple completion and, if it does, outputs a set of maximal gauge algebras in which the sm $$ \mathfrak{sm} $$ ⊕ u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕... model may be embedded. We hope this is a useful tool in pointing the way from sm $$ \mathfrak{sm} $$ ⊕ u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕... models, which have many phenomenological uses, to their unified gauge completions in the ultraviolet.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.