e+e−→π+π−π+π−, K+K−π+π−, and K+K−K+K− cross sections at center-of-mass energies 0.5–4.5 GeV measured with initial-state radiation

We study the process e+e−→π+π−π+π−γ, with a hard photon radiated from the initial state. About 60 000 fully reconstructed events have been selected from 89  fb−1 of BABAR data. The invariant mass of the hadronic final state defines the effective e+e− e+e− center-of-mass energy, so that these data can be compared with the corresponding direct e+e− measurements. From the 4π -mass spectrum, the cross section for the process e+e− →π+π−π+π− is measured for center-of-mass energies from 0.6 to 4.5 GeV. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states K+K−π+π− and K+K−K+K−. We observe the J/ψ in all three final states and measure the corresponding branching fractions. We search for X(3872) in J/ψ(→μ+μ−)π+π− and obtain an upper limit on the product of the e+e− width of the X(3872) and the branching fraction for X(3872)→J/ψπ+π−.