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

We investigate an economical explanation for the $(g-2)_\mu$ anomaly with a neutral vector boson from a spontaneously broken $\mathrm{U}(1)_X$ gauge symmetry. The Standard Model fermion content is minimally extended by 3 right-handed neutrinos. Using a battery of complementary constraints, we perform 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 are viable 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 nonstandard neutrino interactions. Furthermore, we comment on the severe challenges to chiral $\mathrm{U}(1)_X$ solutions and show the severe constraints on a particularly promising such candidate.