Measurement of interference between electromagnetic and strong amplitudes in $\psi (2S)$ decays to two pseudoscalar mesons

Using a sample of $3.08\times {10}^6$ $\psi (2S)$ decays collected at $\sqrt{s}=3.686\mathrm{GeV}$ with the CLEO detector at the Cornell Electron Storage Ring, we have measured the branching fractions for $\psi (2S)$ decays to pseudoscalar pairs ${\pi }^{+}{\pi }^{-}$, $K^{+}{K}^{-}$ and $K_S^0{K}_L^0$. We obtain $\mathcal{B}(\psi (2S)\to {\pi }^{+}{\pi }^{-})<2.1\times {10}^{-5}$ (90% C.L.), $\mathcal{B}(\psi (2S)\to K^{+}{K}^{-})=(6.3\pm 0.6(\mathrm{stat})\pm 0.3(\mathrm{syst}))\times {10}^{-5}$, and $\mathcal{B}(\psi (2S)\to K_S^0{K}_L^0)=(5.8\pm 0.8(\mathrm{stat})\pm 0.4(\mathrm{syst}))\times {10}^{-5}$. The branching fractions allow extraction of the relative phase $\Delta =(95\pm 15)°$ and strength ratio $R=(2.5\pm 0.4)$ of the three-gluon and one-photon amplitudes for these modes.

Figure 1

Scaled energy ($E_{\mathrm{vis}}/\sqrt{s}$) distributions for the $\psi (2S)$ $\to$ (a) ${\pi }^{+}{\pi }^{-}$ and (b) $K^{+}{K}^{-}$ decay modes and the scaled $K_s^0$ energy ($E_{K_S^0}/E_{\mathrm{beam}}$) distribution for the $\psi (2S)$ $\to$ (c) $K_L$$K_S$ decay mode. Signal data, signal simulations, and scaled nonresonant data are shown as points, solid histograms, and dashed histograms, respectively. The signal simulations are normalized to the number of observed events in their respective signal regions.