$J/\psi$ and $\psi (2S)$ Radiative Transitions to ${\eta }_c$

Using $2.45\times {10}^7$ $\psi (2S)$ decays collected with the CLEO-c detector at the Cornell Electron Storage Ring we present the most precise measurements of magnetic dipole transitions in the charmonium system. We measure $\mathcal{B}\mathbf{(}\psi (2S)\to \gamma {\eta }_c\mathbf{)}=(4.32\pm 0.16\pm 0.60)\times {10}^{-3}$, $\mathcal{B}(J/\psi \to \gamma {\eta }_c)/\mathcal{B}\mathbf{(}\psi (2S)\to \gamma {\eta }_c\mathbf{)}=4.59\pm 0.23\pm 0.64$, and $\mathcal{B}(J/\psi \to \gamma {\eta }_c)=(1.98\pm 0.09\pm 0.30)\%$. We observe a distortion in the ${\eta }_c$ line shape due to the photon-energy dependence of the magnetic dipole transition rate. We find that measurements of the ${\eta }_c$ mass are sensitive to the line shape, suggesting an explanation for the discrepancy between measurements of the ${\eta }_c$ mass in radiative transitions and other production mechanisms.

Figure 1

Fits to the photon spectrum in exclusive $J/\psi \to \gamma {\eta }_c$ decays using relativistic Breit-Wigner (dotted line) and modified (solid line) signal line shapes convolved with a 4.8 MeV wide resolution function. Total background is given by the dashed line. The dot-dashed curves indicate two major background components described in the text.

Figure 2

The kinematically fitted photon-energy spectra from $\psi (2S)\to \gamma {\eta }_c$ for individual ${\eta }_c$ decay modes.

Figure 3

(a) The kinematically fitted photon spectrum from the sum of exclusive $\psi (2S)\to \gamma {\eta }_c$ modes with a polynomial fit to the background (solid line for the regions included in the fit; dotted line elsewhere). (b) The photon-energy spectrum that has not been adjusted by the kinematic fit with the same background shape as (a) overlaid. (c) The fit to the inclusive photon spectrum in $\psi (2S)$ decay. The signal shape (solid line) is described in the text. The background is given by the dashed line. (d) The background subtracted inclusive photon spectrum with the signal shape overlaid (solid line).