Muon g-2, Rare Kaon Decays, and Parity Violation from Dark Bosons

The muon g-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-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 -> 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 muon g-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.