Muon $g-2$ anomaly and dark leptonic gauge boson

One of the major motivations to search for a dark gauge boson of MeV–GeV scale is the long-standing $g_{\mu }-2$ anomaly. Because of active searches such as fixed target experiments and rare meson decays, the $g_{\mu }-2$ favored parameter region has been rapidly reduced. With the most recent data, it is practically excluded now in the popular dark photon model. We overview the issue and investigate a potentially alternative model based on the gauged lepton number or $U(1{)}_L$. The $g_{\mu }-2$ favored parameter region of the $U(1{)}_L$ survives all the constraints that were critical in the dark photon case, yet it is disfavored by the new constraints from the large flux neutrino experiments.

Figure 1

Constraints on the dark photon parameter space (a) for the typical case of $\mathrm{Br}(Z^{\prime }\to {\ell }^{+}{\ell }^{-})\approx 1$, and (b) for the very light dark matter case of $\mathrm{Br}(Z^{\prime }\to \text{invisible})=1$. The figures are based on Ref. [13] with the updates from new data and cosmetic changes. The $g_{\mu }-2$ favored region (green band) in typical case (a) is practically closed with the new data.

Figure 2

Constraints on the parameter space of the dark leptonic gauge boson in the $U(1{)}_L$ model.