The e+ e- --> pi+ p- pi+ pi-, k+ k- pi+ pi-, and k+ k- k+ k- cross sections at center-of-mass energies 0.5 gev to 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 Jψ(→ 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) → Jψπ+π-. © 2005 The American Physical Society.