First energy scan measurement of $e^{+}e^{-}\to K^{+}K^{-}$ around the $\psi(2S)$ resonance

Abstract

We report the first measurement of the $e^{+}e^{-}\to K^{+}K^{-}$ cross sections around the $\psi(2S)$ resonance using the energy scan method. The analysis is based on $e^{+}e^{-}$ collision data corresponding to an integrated luminosity of 495~pb$^{-1}$ collected with the BESIII detector at BEPCII. By analyzing the cross section line-shape, we extract the relative phase $\Phi$ between the strong and electromagnetic amplitudes of the $\psi(2S)$ resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the $\psi(2S)$ resonance and the continuum is zero. Two distinct solutions for the branching fraction $\mathcal{B}$ of $\psi(2S)\to K^{+}K^{-}$ are observed: a constructive interference solution with $\mathcal{B}=(7.49\pm0.41)\times10^{-5}$ and $\Phi=(110.1 \pm6.7)^\circ$, and a destructive interference solution with $\mathcal{B}=(10.94\pm0.48)\times10^{-5}$ and $\Phi=(-106.8\pm5.7)^\circ$. A significant correlation between $\Phi$ and $\mathcal{B}$ is established, demonstrating that interference effects must be taken into account in the $\psi(2S)$ branching fraction measurements. Additionally, the first results for both the $\psi(2S)$ strong form factor, which characterizes the strong coupling between $\psi(2S)$ and $K^{+}K^{-}$, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are here reported.