Existing data on the $e^{+}{e}^{-}\to K^{+}{K}^{-}$ cross section at the center-of-mass energy above 2.6 GeV are fitted with a sum of $\psi (3770)$ resonant and continuum contributions. Two solutions for the resonance production cross section are found with a significance of $3.2\sigma$. Data on the $e^{+}{e}^{-}\to K_S{K}_L$ cross section are used to resolve the ambiguity and to further constrain the values of the $e^{+}{e}^{-}\to \psi (3770)\to K^{+}{K}^{-}$ cross section and the interference phase. They are found to be ${\sigma }_{\psi (3770)}=0.073_{-0.044}^{+0.061}\mathrm{pb}$ and $\varphi =(309_{-35}^{+17}{)}^{°}$, respectively. The same fitting procedure for the $\psi (4160)$ resonance leads to the upper limit on the $e^{+}{e}^{-}\to \psi (4160)\to K^{+}{K}^{-}$ cross section ${\sigma }_{\psi (4160)}<0.062\mathrm{pb}$ at the 90% confidence level.

• Received 19 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.054024