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We investigate an economical explanation for the $(g-2)_\mu$ anomaly with aneutral vector boson from a spontaneously broken $\mathrm{U}(1)_X$ gaugesymmetry. The Standard Model fermion content is minimally extended by 3right-handed neutrinos. Using a battery of complementary constraints, weperform a thorough investigation of the renormalizable, quark flavor-universal,vector-like $\mathrm{U}(1)_X$ models, allowing for arbitrary kinetic mixing.Out of 419 models with integer charges not greater than ten, only 7 models areviable solutions, describing a narrow region in model space. These are either$L_\mu-L_\tau$ or models with a ratio of electron to baryon number close to$-2$. The key complementary constraints are from the searches for nonstandardneutrino interactions. Furthermore, we comment on the severe challenges tochiral $\mathrm{U}(1)_X$ solutions and show the severe constraints on aparticularly promising such candidate.

On $(g-2)_\mu$ From Gauged $\mathrm{U}(1)_X$