Imperfect Mirrors of the Standard Model

TL;DR

This paper proposes a method to construct chiral, anomaly-free gauge theories inspired by the Standard Model, exploring their properties and potential implications for neutrino masses and dark matter.

Contribution

It introduces a systematic approach to building 'imperfect' Standard Model-like theories using subgroups of simple Lie groups, expanding the landscape of viable particle physics models.

Findings

Constructed various anomaly-free chiral gauge theories based on $SO(10)$ and $E_6$.

Identified properties of these theories and their potential relevance to neutrino masses and dark matter.

Provided insights into how these models could address phenomenological questions.

Abstract

Inspired by the Standard Model of particle physics, we discuss a mechanism for constructing chiral, anomaly-free gauge theories. The gauge symmetries and particle content of such theories are identified using subgroups and complex representations of simple anomaly-free Lie groups, such as $SO(10)$ or $E_6$. We explore, using mostly $SO(10)$ and the $\mathbf{16}$ representation, several of these "imperfect copies" of the Standard Model, including $U(1)^N$ theories, $SU(5)\otimes U(1)$ theories, $SU(4)\otimes U(1)^2$ theories with 4-plets and 6-plets, and chiral $SU(3)\otimes SU(2)\otimes U(1)$. A few general properties of such theories are discussed, as well as how they might shed light on nonzero neutrino masses, the dark matter puzzle, and other phenomenologically relevant questions.