Photon transitions in $\psi (2S)$ decays to ${\chi }_{cJ}(1P)$ and ${\eta }_c(1S)$

We have studied the inclusive photon spectrum in $\psi (2S)$ decays using the CLEO III detector. We present the most precise measurements of electric dipole (E1) photon transition rates for $\psi (2S)\to \gamma {\chi }_{cJ}(1P)$ ($J=0,1,2$). We also confirm the hindered magnetic dipole (M1) transition, $\psi (2S)\to \gamma {\eta }_c(1S)$. However, the direct M1 transition $\psi (2S)\to \gamma {\eta }_c(2S)$ observed by the Crystal Ball as a narrow peak at a photon energy of 91 MeV is not found in our data.

Figure 1

Going from bottom to top, the histograms show the photon energy spectra at the $\psi (2S)$ resonance omitting those photons which, with another photon in the event, form a ${\pi }^0$ candidate with $\cos {\theta }_{\gamma \gamma }$ exceeding: $-1$;, i.e., maximal ${\pi }^0$ suppression (solid), 0.3 (dashed), 0.5 (solid), 0.7 (dashed), 1.0;, i.e., no ${\pi }^0$ suppression (solid). The first three peaks correspond to E1 photon transitions: $\psi (2S)\to \gamma {\chi }_{cJ}(1P)$, $J=2$ ($128$ MeV), $1$ ($172$ MeV) and $0$ ($262$ MeV). The fourth peak around $400$ MeV is an overlap of two E1 photon lines: ${\chi }_{cJ}(1P)\to \gamma J/\psi (1S)$, $J=1$ and $2$. A small peak at $646$ MeV is due to hindered M1 photon transition: $\psi (2S)\to \gamma {\eta }_c(1S)$.

Figure 2

Fit of $\psi (2S)\to \gamma {\chi }_{cJ}(1P)$ ($J=2,1,0$) photon lines to the data. The points represent the data. The solid line represents the fit. The dashed line represents total fitted background. The dotted line represents the polynomial background alone, without the contributions from charged particles and the decays $J/\psi (1S)\to \gamma {\eta }_c(1S)$. The background-subtracted data (points) and the fitted photon lines superimposed (solid line) are shown at the bottom.

Figure 3

Fit of $\psi (2S)\to \gamma {\eta }_c(1S)$ photon line to the data. The points represent the data. The solid line represents the fit. The dashed line represents the total fitted background. The background-subtracted data (points with error bars) and the fitted photon line superimposed (solid line) are shown at the bottom.