The $e^+e^- \to 3(\pi^+ \pi^-), 2(\pi^+ \pi^- \pi^0)$ and $K^+ K^- 2(\pi^+ \pi^-)$ 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.