A Survey of Family Unification Models with Bifundamental Matter

TL;DR

This paper systematically explores models unifying Standard Model families using bifundamental matter in product gauge groups, identifying 151 unique models with potential experimental signatures near the electroweak scale.

Contribution

It provides an exhaustive enumeration of family unification models with bifundamental fermions within certain gauge groups, including the identification of models with vector-like BSM particles and potential collider signatures.

Findings

Identified 151 unique models with family unification.

Found 9 models with only vector-like BSM particles.

Predicted BSM particles with masses near the electroweak scale.

Abstract

Extensions of the Standard Model have been attempted from the bottom up and from the top down yet there remains a largely unexplored middle ground. In this paper, using the Mathematica package LieART, we exhaustively enumerate embeddings of the Standard Model within the class of theories with bifundamental fermions in product gauge group SU(a)XSU(b)XSU(c) with no more generators than E6, while achieving SM family unification rather than replication. We incorporate simple phenomenological constrains and find 151 unique models, including 9 that have only vector-like particle content beyond-the-Standard Model (BSM) particles, which we conjecture belong to 5 infinite families of such models. We describe the potentially most viable models: namely, the 9 with strictly vector-like BSM content along with the 29 models we found with no more than 30 additional BSM chiral particles. These include models with fractional electric charge color singlets, and hence magnetic monopoles with multiple Dirac charge. This latter collection of models predicts chiral particles with masses near the electroweak scale accessible to current and future collider experiments.