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 $U^{\prime }$ that couples to quarks in the decay chain $D^{*+}\to D^0{\pi }^{+},D^0\to K_S^0\eta ,\eta \to U^{\prime }\gamma$, $U^{\prime }\to {\pi }^{+}{\pi }^{-}$. No signal is found and we set a mass-dependent limit on the baryonic fine structure constant of ${10}^{-3}-{10}^{-2}$ in the $U^{\prime }$ mass range of 290 to $520\mathrm{MeV}/c^2$. This analysis is based on a data sample of $976{\mathrm{fb}}^{-1}$ collected by the Belle experiment at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

Invariant mass of the $K_S^0\eta$ combinations (left) and the $D^{*}-D^0$ mass difference (right) for $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ decays.

Figure 2

Invariant mass distribution of the ${\pi }^{+}{\pi }^{-}\gamma$ combinations (points with error bars), fit result (solid curve), and combinatorial background component (dashed line) of the fit function. Arrows with lines indicate boundaries of the signal and sideband regions.

Figure 3

${\pi }^{+}{\pi }^{-}$ invariant mass distribution from the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ signal (points with error bars), the fitted differential decay rate described in Eq. (1) (solid curve), and an example $U^{\prime }$ signal at a mass of $400\mathrm{MeV}/c^2$ from $\eta \to U^{\prime }\gamma$, $U^{\prime }\to {\pi }^{+}{\pi }^{-}$ (histogram with arbitrary normalization).

Figure 4

Computed 95% upper limit on the baryonic fine structure constant ${\alpha }_{U^{\prime }}$ as a function of the unknown $U^{\prime }$ mass (solid curve).