Muong−2, rare kaon decays, and parity violation from dark bosons

Abstract

The muon ${g}_{\ensuremath{\mu}}\ensuremath{-}2$ 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 ${g}_{e}\ensuremath{-}2$, pion Dalitz decay, and other direct production data disfavor that explanation if the ${Z}_{d}$ mainly decays into ${e}^{+}{e}^{\ensuremath{-}}$, ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Implications of a dominant invisible ${Z}_{d}$ decay channel, such as light dark matter, along with the resulting strong bounds from the rare $K\ensuremath{\rightarrow}\ensuremath{\pi}$ + missing energy decay are examined. The $K$ decay constraints may be relaxed if destructive interference effects due to $Z\ensuremath{-}{Z}_{d}$ mass mixing are included. In that scenario, we show that accommodating the ${g}_{\ensuremath{\mu}}\ensuremath{-}2$ 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.