Search for a dark vector gauge boson decaying to ${\pi }^{+}{\pi }^{-}$ using $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ decays

We report a search for a dark vector gauge boson $U^{\mathrm{\prime }}$ that couples to quarks in the decay chain $D^{*+} \to D^0 \pi^+, D^0 \to K^0_S \eta, \eta \to U^\prime \gamma$,$U^\prime \to \pi^+ \pi^-$. No signal is found and we set a mass-dependent limit on the baryonic fine structure constant of $10^{-3} - 10^{-2}$inthe$U^\prime$massrangeof290to520MeV\mathrm{/}$c^2$. This analysis is based on a data sample of 976 fb${}^{-1}$ collected by the Belle experiment at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.