Cross sections for the reactions e⁺e⁻→ K_s^0 K_L^0, K_s^0 K_L^0 π⁺π⁻, K_s^0 K_s^0 π⁺π⁻, K_s^0 K_s^0 K⁺ K⁻ from events with initial-state radiation

We study the processes e⁺e⁻ → K_s^0 K_L^0γ, K_s^0 K_L^0π⁺π⁻γ, K_s^0 K_s^0 π⁺ π⁻ γ, K_s^0 K_s^0 K⁺ K⁻ γ, where the photon is radiated from the initial state. providing cross section measurements for the hadronic states over a continuum of center-of-mass energies. The results are based on 469 fb−1 of data collected with the BABAR detector at SLAC. We observe the ϕ(1020) resonance in the K_s^0 K_L^0 final state and measure the product of its electronic width and branching fraction with about 3% uncertainty. We present a measurement of the e⁺e⁻ → K_s^0 K_L^0 cross section in the energy range from 1.06 to 2.2 GeV and observe the production of a resonance at 1.67 GeV. We present the first measurements of the e⁺e⁻ → K_s^0 K_L^0 π⁺π⁻ and K_s^0 K_s^0 K⁺ K⁻ cross sections and study the intermediate resonance structures. We obtain the first observations of J/ψ decay to the K_s^0 K_L^0 π⁺π⁻, K_s^0 K_s^0 π⁺π⁻, and K_s^0 K_s^0 K⁺ K⁻ final states.