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

Abstract

We report the first measurement of the $e^{+}e^{-}\to K^{+}K^{-}$ cross sections around the $ψ(2S)$ 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 $Φ$ between the strong and electromagnetic amplitudes of the $ψ(2S)$ resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the $ψ(2S)$ resonance and the continuum is zero. Two distinct solutions for the branching fraction $\mathcal{B}$ of $ψ(2S)\to K^{+}K^{-}$ are observed: a constructive interference solution with $\mathcal{B}=(7.49\pm0.41)\times10^{-5}$ and $Φ=(110.1 \pm6.7)^\circ$, and a destructive interference solution with $\mathcal{B}=(10.94\pm0.48)\times10^{-5}$ and $Φ=(-106.8\pm5.7)^\circ$. A significant correlation between $Φ$ and $\mathcal{B}$ is established, demonstrating that interference effects must be taken into account in the $ψ(2S)$ branching fraction measurements. Additionally, the first results for both the $ψ(2S)$ strong form factor, which characterizes the strong coupling between $ψ(2S)$ and $K^{+}K^{-}$, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are here reported.

Figures (4)

• Figure 1: (a) Distribution of $M_{K^+K^-}$ of the accepted candidates at $\sqrt{s}=3.6865$ GeV. (b) Distribution of cosine of the polar angle $\theta$ of $K^{+}$ in the signal region for all energy points. The dots with error bars represent the data. The red dashed curve and histogram are the signal MC sample, and the brown dotted line and filled histogram are the background events of $e^{+}e^{-}\to\mu^{+}\mu^{-}$, respectively. The region between the arrows denotes the signal region.
• Figure 2: The $e^{+}e^{-}\to K^{+}K^{-}$ cross section data (black points) are shown with statistical and systematic uncertainties. The blue line is the fit result, with the dotted line indicating the continuum. The dashed and dash-dotted lines represent resonance and interference contributions, respectively.
• Figure 3: Contours in the $\mathcal{B}(\psi(2S)\to K^{+}K^{-})$ versus the relative phase $\Phi$ plane.
• Figure 4: Comparison of our measured form factors (blue points with error bars) with the previous results from BESIII ref_exp_KFF3 (black triangles with error bars) and BaBar ref_exp_KFF1 (hole squares with error bars).