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-.