The muon $g_{\mu }-2$ discrepancy between theory and experiment may be explained by a light vector boson $Z_d$ that couples to the electromagnetic current via kinetic mixing with the photon. We illustrate how the existing electron $g_e-2$, pion Dalitz decay, and other direct production data disfavor that explanation if the $Z_d$ mainly decays into $e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$. Implications of a dominant invisible $Z_d$ decay channel, such as light dark matter, along with the resulting strong bounds from the rare $K\to \pi$ + missing energy decay are examined. The $K$ decay constraints may be relaxed if destructive interference effects due to $Z-Z_d$ mass mixing are included. In that scenario, we show that accommodating the $g_{\mu }-2$ data through relaxation of $K$ decay constraints leads to interesting signals for dark parity violation. As an illustration, we examine the alteration of the weak mixing angle running at low $Q^2$, which can be potentially observable in polarized electron scattering or atomic physics experiments.

• Received 21 February 2014

DOI:https://doi.org/10.1103/PhysRevD.89.095006