Measurement of the ${\eta }^{\prime }$-Meson Mass using $J/\psi \to \gamma {\eta }^{\prime }$

We measure the mass of the ${\eta }^{\prime }$ meson using $\psi (2S)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to \gamma {\eta }^{\prime }$ events acquired with the CLEO-c detector operating at the CESR $e^{+}{e}^{-}$ collider. Using three decay modes, ${\eta }^{\prime }\to {\rho }^0\gamma$, ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$ with $\eta \to \gamma \gamma$, and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$ with $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$, we find $M_{{\eta }^{\prime }}=957.793\pm 0.054\pm 0.036\mathrm{MeV}$, in which the uncertainties are statistical and systematic, respectively. This result is consistent with but substantially more precise than the current world average.

Figure 1

Distributions of the fit quality for the kinematic constraint procedures described in the text, for, from top to bottom, modes $A$, $B$, and $C$, and, from left to right, $J/\psi$ vertex fit, $J/\psi$ mass fit, $\psi (2S)$ vertex fit, and $\psi (2S)$ four-momentum fit. Arrows indicate nominal selection criteria. The solid line histogram represents the signal MC prediction normalized to the number of events in the data.

Figure 2

Distributions of ${\eta }^{\prime }$-candidate masses (left) for modes A (top), B (middle), and C (bottom). On the right, masses of intermediate particles: the ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ mass for mode $A$, the $\eta \to \gamma \gamma$ mass for mode $B$, and the ${\pi }^0\to \gamma \gamma$ mass for mode $C$. Symbols are defined as in Fig. 1.

Figure 3

Distributions of $\delta$ for, from top to bottom, modes $A$, $B$, $C$, and $D$ (see text), with the data represented by the points with error bars and the Gaussian fit overlaid. The solid line portion of the Gaussian curve indicates the mass window used for the fit and the dashed portions its extension. The solid line histogram represents MC simulation of signal, normalized as in Figs. 1 and 2.