Muon Anomaly and Dark Parity Violation

The muon anomalous magnetic moment exhibits a $3.6\sigma$ discrepancy between experiment and theory. One explanation requires the existence of a light vector boson, $Z_d$ (the dark $Z$), with mass 10–500 MeV that couples weakly to the electromagnetic current through kinetic mixing. Support for such a solution also comes from astrophysics conjectures regarding the utility of a $U(1{)}_d$ gauge symmetry in the dark matter sector. In that scenario, we show that mass mixing between the $Z_d$ and ordinary $Z$ boson introduces a new source of “dark” parity violation, which is potentially observable in atomic and polarized electron scattering experiments. Restrictive bounds on the mixing $(m_{Z_d}/m_Z)\delta$ are found from existing atomic parity violation results, ${\delta }^2<2\times {10}^{-5}$. Combined with future planned and proposed polarized electron scattering experiments, a sensitivity of ${\delta }^2\sim {10}^{-6}$ is expected to be reached, thereby complementing direct searches for the $Z_d$ boson.

Figure 1

Dark $Z$ boson exclusion regions (partly adapted from Ref. 9) in the ($m_{Z_d}$, ${\epsilon }^2$) plane along with the band that explains the $\Delta a_{\mu }$ discrepancy (90% C.L.) and exclusion regions from atomic parity violation (above the lines) for $Z\mathrm{\text{−}}{Z}_d$ mixing $\delta$ values.

Figure 2

Dark $Z$ boson exclusion regions from various parity violating experiments (existing and proposed) and their combined sensitivity for ${\delta }^2={10}^{-5}$ (left) and ${10}^{-6}$ (right) at 90% C.L.