Search for ${\eta }^{\prime }$ Bound Nuclei in the ${}^{12}\mathrm{C}(\gamma ,p)$ Reaction with Simultaneous Detection of Decay Products

We measured missing mass spectrum of the ${}^{12}\mathrm{C}(\gamma ,p)$ reaction for the first time in coincidence with potential decay products from ${\eta }^{\prime }$ bound nuclei. We tagged an ($\eta +p$) pair associated with the ${\eta }^{\prime }N\to \eta N$ process in a nucleus. After applying kinematical selections to reduce backgrounds, no signal events were observed in the bound-state region. An upper limit of the signal cross section in the opening angle $\cos {\theta }_{\mathrm{lab}}^{\eta p}<-0.9$ was obtained to be $2.2\mathrm{nb}/\mathrm{sr}$ at the 90% confidence level. It is compared with theoretical cross sections, whose normalization ambiguity is suppressed by measuring a quasifree ${\eta }^{\prime }$ production rate. Our results indicate a small branching fraction of the ${\eta }^{\prime }N\to \eta N$ process and/or a shallow ${\eta }^{\prime }$-nucleus potential.

Figure 1

(a) The $2\gamma$ invariant mass distribution around the $\eta$ mass and (b) the excitation function of the $(\eta +p_s)$ coincidence data. The region in $\pm 2.5\sigma$ from the invariant mass peak is indicated by the blue-dashed lines.

Figure 2

The two dimensional plot of $\cos {\theta }_{\mathrm{lab}}^{\eta }$ vs $E_{\mathrm{ex}}-E_0^{{\eta }^{\prime }}$ of the $(\eta +p_s)$ coincidence data after applying the kinematical cuts (a)–(c). The region to search for signals is shown by red hatching.

Figure 3

The $E_{\gamma }$ dependence of ${(d\sigma /d\mathrm{\Omega })}_{\exp }^{{\eta }^{\prime }\text{esc}}$ (black circles) and ${(d\sigma /d\mathrm{\Omega })}_{\text{theory}}^{{\eta }^{\prime }\text{esc}}$ (red lines) in $0<E_{\mathrm{ex}}-E_0^{\gamma \gamma }<50\mathrm{MeV}$. The original ${(d\sigma /d\mathrm{\Omega })}_{\text{theory}}^{{\eta }^{\prime }\text{esc}}$ based on Ref. [27] without using the Fermi averaging method is shown by the blue line. The theoretical calculations after the normalization are shown by green lines.

Figure 4

The experimental upper limit of ${(d\sigma /d\mathrm{\Omega })}_{\exp }^{\eta +p_s}$ at the 90% confidence level, and ${(d\sigma /d\mathrm{\Omega })}_{\text{theory}}^{\eta +p_s}$ as a function of ${\text{Br}}_{{\eta }^{\prime }N\to \eta N}$.