Solving local anomaly equations in gauge-rank extensions of the Standard Model

TL;DR

This paper provides a comprehensive solution to local gauge anomaly cancellation conditions in extended Standard Model frameworks with additional singlet fermions, ensuring theoretical consistency for various charge assignment scenarios.

Contribution

It offers a general method to solve anomaly cancellation conditions in gauge-rank extended models, covering both universal and non-universal family charge cases.

Findings

Solutions exist for all ACCs when n ≥ 5 (non-universal) or n ≥ 3 (universal).

A general solution is found for models with a single family carrying charges, for any n.

The paper clarifies conditions under which anomaly cancellation is achievable in extended gauge models.

Abstract

We consider local (or perturbative) gauge anomalies in models which extend the rank of the Standard Model (SM) gauge group and the chiral fermion content only by $n$ SM singlets. We give a general solution to the anomaly cancellation conditions (ACCs) of an additional $U(1)$ subgroup for the ACCs that involve only SM fermions and we examine whether a corresponding solution exists for the remaining ACCs. We show that a solution to the remaining ACCs always exists for $n \geq 5$ in the family non-universal case or $n \geq 3$ in the family-universal case. In the special case where only a single family carries non-vanishing charges, we find a general solution to all ACCs, for any value of $n$.