The e+e-→3(π+π-), 2(π+π-π0) and K+K-2(π+π-) cross sections at center-of-mass energies from production threshold to 4.5 GeV measured with initial-state radiation

We study the processes e+e-→3(π+π-)γ, 2(π+π-π0)γ and K+K-2(π+π-)γ, with the photon radiated from the initial state. About 20 000, 33 000 and 4000 fully reconstructed events, respectively, have been selected from 232  fb-1 of BABAR data. The invariant mass of the hadronic final state defines the effective e+e- center-of-mass energy, so that these data can be compared with the corresponding direct e+e- measurements. From the 3(π+π-), 2(π+π-π0) and K+K-2(π+π-) mass spectra, the cross sections for the processes e+e-→3(π+π-), e+e-→2(π+π-π0) and e+e-→K+K-2(π+π-) are measured for center-of-mass energies from production threshold to 4.5 GeV. The uncertainty in the cross section measurement is typically 6%–15%. We observe a structure at 1.9 GeV in both cross sections and a resonance structure with mass 1645±0.008  GeV/c2 and width 0.114±0.014  GeV when the ω(782)η final state is extracted. We observe the J/ψ in all these final states and measure the corresponding branching fractions.