A $\nu$ Supersymmetric Anomaly-free Atlas

TL;DR

This paper systematically classifies all anomaly-free charge assignments for an extended supersymmetric model with an extra U(1) gauge group, providing a comprehensive resource for model building and phenomenology.

Contribution

It offers a complete enumeration of anomaly-free U(1)_X charge assignments up to a maximum charge, including an analytic parameterization for unbounded charges.

Findings

All anomaly-free charge assignments up to Q_max=10 are provided.

Publicly available list of charge assignments on Zenodo.

Analytic parameterization of solutions for unbounded charges.

Abstract

Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional $U(1)_X$ gauge group. Chiral fermions' charge assignments under $U(1)_X$ are constrained to cancel local anomalies in the extension and they determine the structure and phenomenology of it. We provide all anomaly-free charge assignments up to a maximum absolute charge of $Q_\text{max}=10$, assuming that the chiral superfield content of the model is that of the MSSM plus up to three Standard Model (SM) singlet superfields. The fermionic components of these SM singlets may play the r\^{o}le of right-handed neutrinos, whereas one of the scalar components may play the r\^{o}le of the flavon, spontaneously breaking $U(1)_X$. Easily scanned lists of the charge assignments are made publicly available on Zenodo. For the case where no restriction is placed upon $Q_\text{max}$, we also provide an analytic parameterisation of the general solution using simple techniques from algebraic geometry.