Using the upgraded Beijing Spectrometer (BESII), we have measured the total cross section for $e^+e^-$ annihilation into hadronic final states at center-of-mass energies of 2.6, 3.2, 3.4, 3.55, 4.6 and 5.0 GeV. Values of $R$, $\sigma(e^+e^-\to {hadrons})/\sigma(e^+e^-\to\mu^+\mu^-)$, are determined.
The cross sections of the processes $e^+ e^- \to K^+ K^- J/\psi$ and $K_S^0K_S^0J/\psi$ are measured via initial state radiation at center-of-mass energies between the threshold and 6.0~GeV using a data sample of 980~fb$^{-1}$ collected with the Belle detector on or near the $\Upsilon(nS)$ resonances, where $n=$1, 2, ..., 5. The cross sections for $e^+ e^- \to K^+ K^- J/\psi$ are at a few pb level and the average cross section for $e^+ e^- \to K_S^0K_S^0J/\psi$ is $1.8\pm 0.6 (\rm stat.)\pm 0.3 (\rm syst.)$~pb between 4.4 and 5.2~GeV. All of them are consistent with previously published results with improved precision. A search for resonant structures and associated intermediate states in the cross section of the process $e^+ e^- \to K^+ K^- J/\psi$ is performed.
The $e^+e^-\to K^+K^-$ cross section and charged-kaon electromagnetic form factor are measured in the $e^+e^-$ center-of-mass energy range ($E$) from 2.6 to 8.0 GeV using the initial-state radiation technique with an undetected photon. The study is performed using 469 fb$^{-1}$ of data collected with the BABAR detector at the PEP-II $e^+e^-$ collider at center-of-mass energies near 10.6 GeV. The form factor is found to decrease with energy faster than $1/E^2$, and approaches the asymptotic QCD prediction. Production of the $K^+K^-$ final state through the $J/\psi$ and $\psi(2S)$ intermediate states is observed. The results for the kaon form factor are used together with data from other experiments to perform a model-independent determination of the relative phases between single-photon and strong amplitudes in $J/\psi$ and $\psi(2S)\to K^+K^-$ decays. The values of the branching fractions measured in the reaction $e^+e^- \to K^+K^-$ are shifted relative to their true values due to interference between resonant and nonresonant amplitudes. The values of these shifts are determined to be about $\pm5\%$ for the $J/\psi$ meson and $\pm15\%$ for the $\psi(2S)$ meson.