Search for intermediate resonances and dark gauge bosons in $J/\psi \to \gamma {\pi }^0{\eta }^{\prime }$

We report on an analysis of the decay $J/\psi \to \gamma {\pi }^0{\eta }^{\prime }$ using a sample of $(1310.6\pm 7.0)\times {10}^{6}J/\psi$ events collected with the BESIII detector. We search for the $CP$-violating process ${\eta }_c\to {\pi }^0{\eta }^{\prime }$ and a dark gauge boson $U^{\prime }$ in $J/\psi \to U^{\prime }{\eta }^{\prime },U^{\prime }\to \gamma {\pi }^0,{\pi }^0\to \gamma \gamma$. No evidence of an ${\eta }_c$ signal is observed in the ${\pi }^0{\eta }^{\prime }$ invariant-mass spectrum and the upper limit of the branching fraction is determined to be $5.6\times {10}^{-5}$ at the 90% confidence level. We also find no evidence of $U^{\prime }$ production and set upper limits at the 90% confidence level on the product branching fraction $\mathcal{B}(J/\psi \to U^{\prime }{\eta }^{\prime })\times \mathcal{B}(U^{\prime }\to {\pi }^0\gamma )$ in the range between $(0.8-6.5)\times {10}^{-7}$ for $0.2\le m_{U^{\prime }}\le 2.1\mathrm{GeV}/c^2$. In addition, we study the process $J/\psi \to \omega {\eta }^{\prime }$ with $\omega \to \gamma {\pi }^0$. The branching fraction of $J/\psi \to \omega {\eta }^{\prime }$ is found to be $(1.87\pm 0.09\pm 0.12)\times {10}^{-4}$, where the first uncertainty is statistical and the second is systematic, with a precision that is improved by a factor of 1.4 over the previously published BESIII measurement.

Figure 1

The ${\pi }^0{\eta }^{\prime }$-mass spectrum. The black dots with error bars are data. (a) The histogram with the red line represents the extracted line shape of the signal process $J/\psi \to \gamma {\eta }_c$. The yellow area shows the MC distribution of $J/\psi \to \gamma {\pi }^0{\eta }^{\prime }$, the green area corresponds to the MC distribution of $J/\psi \to \gamma {\eta }^{\prime }$, the blue area shows the MC distribution of $J/\psi \to \omega {\eta }^{\prime }$, and the gray area represents the non-${\eta }^{\prime }$ contributions obtained from ${\eta }^{\prime }$-sideband data. (b) Fit to the $M_{{\pi }^0{\eta }^{\prime }}$ with a free signal yield. The red histogram shows the contribution of the ${\eta }_c$ signal, the green dashed line represents the $J/\psi \to \gamma {\eta }^{\prime }({\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-},\eta \to \gamma \gamma )$ background contribution, and the pink dashed line depicts other nonpeaking background contributions described by a first-order Chebyshev polynomial.

Figure 2

The $\gamma {\pi }^0$ invariant-mass spectrum. The black dots with error bars are data. The various shaded histograms are described in the caption of Fig. 1.

Figure 3

(a) The number of extracted signal events, (b) Statistical signal significance, and (c) the detection efficiency as a function of $M_{U^{\prime }}$ in the range of $0.2\le M_{U^{\prime }}\le 2.1\mathrm{GeV}/c^2$. The region of the $\omega$ resonance is indicated by the gray band and excluded from the $U^{\prime }$ search.

Figure 4

A two-dimensional distribution of the reconstructed ${\pi }^{+}{\pi }^{-}\eta$ and $\gamma {\pi }^0$ masses. The size of each box scales with the number of events found in that particular bin.

Figure 5

Projection plots of (a) $M_{\gamma {\pi }^0}$ and (b) $M_{{\pi }^{+}{\pi }^{-}\eta }$ distributions in the decay chain of $J/\psi \to \omega {\eta }^{\prime },\omega \to \gamma {\pi }^0,{\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$. The dots with error bars correspond to data; the solid curve shows the result of the fit including both signal and background distributions. The long-dashed curve corresponds to the contribution of the $\omega {\eta }^{\prime }$ signal, the dotted curve shows the contribution of the non-${\eta }^{\prime }$ peaking background, the dot-dashed curve shows the contribution of the non-$\omega$ peaking background, and the short-dashed curve represents the non-$\omega {\eta }^{\prime }$ background part.

Figure 6

The distribution of the normalized likelihood scan for $J/\psi \to \gamma {\eta }_c({\eta }_c\to {\pi }^0{\eta }^{\prime })$ candidates. The blue and red curves describe the smoothed likelihood curves before and after the inclusion of the multiplicative systematic uncertainty. The blue and red arrows show the upper limit on the signal yield at 90% C.L.

Figure 7

The upper limit at the 90% C.L. on the product branching fraction $\mathcal{B}(J/\psi \to U^{\prime }{\eta }^{\prime })\times \mathcal{B}(U^{\prime }\to {\pi }^0\gamma )$. The region of the $\omega$ resonance indicated by the gray band is excluded from the $U^{\prime }$ search.