Lowest Dimensional Portals to SU($N$) Exotics

TL;DR

This paper systematically classifies the simplest interaction operators ('portals') between hypothetical exotic matter fields charged under SU(N) gauge groups and Standard Model particles, extending previous SU(3) results to general SU(N).

Contribution

It provides a comprehensive analysis of lowest-dimensional portal operators for SU(N) representations and introduces a Python tool for automatic construction of these operators.

Findings

Classified all lowest-dimensional portal operators for SU(3) and extended to SU(N).

Developed and released 'tessellation', a Python code for constructing portal operators.

Facilitates exploration of exotic matter interactions in grand unified theories.

Abstract

New matter fields charged under the strong nuclear force would have dramatic phenomenological implications. Here, we systematically explore how these new states, which we postulate belong to some representation of SU(3) of quantum chromo-dynamics, could interact with Standard Model fields: We analyze all lowest-dimensional "portal" operators for any SU(3) representation and, motivated by grand unification, we extend our results to SU($N$), for $N>3$. We provide a publicly available python code, "tessellation", that automatically constructs said lowest-dimensional portal operators for any new exotic matter field charged under SU($N$) for any $N$.