A $\nu$ Supersymmetric Anomaly-free Atlas

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 role of right-handed neutrinos, whereas one of the scalar components may play the role 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.