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(pi(+)pi(-))gamma, 2(pi(+)pi(-)pi(0))gamma and K(+)K(-)2(pi(+)pi(-))gamma, 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(pi(+)pi(-)), 2(pi(+)pi(-)pi(0)) and K(+)K(-)2(pi(+)pi(-)) mass spectra, the cross sections for the processes e(+)e(-)-> 3(pi(+)pi(-)), e(+)e(-)-> 2(pi(+)pi(-)pi(0)) and e(+)e(-)-> K(+)K(-)2(pi(+)pi(-)) 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/c(2) and width 0.114 +/- 0.014 GeV when the omega(782)eta final state is extracted. We observe the J/psi in all these final states and measure the corresponding branching fractions.