Uniqueness of a recently proposed U(1) gauge extension

Abstract

Consider the addition of a right-handed SU(2) fermion multiplet (with neither color nor hypercharge) to each family of quarks and leptons. The resultant theory admits a new U(1) gauge symmetry only if the additional multiplet is a singlet $N_R$, which corresponds to the well-known case of $U(1)_{B-L}$, or a triplet $(\Sigma^+, \Sigma^0, \Sigma^-)$, which corresponds to the proposal of hep-ph/0112232. This disproves the assertion that the latter is somehow a ``trivial'' or ``expected'' discovery.