The e(+)e(-)-> 2(pi(+)pi(-))pi(0), 2(pi(+)pi(-))eta, K(+)K(-)pi(+)pi(-)pi(0) and K(+)K(-)pi(+)pi(-)eta cross sections measured with initial-state radiation

We study the processes e(+)e(-)-> 2(pi(+)pi(-))pi(0)gamma, 2(pi(+)pi(-))eta gamma, K(+)K(-)pi(+)pi(-)pi(0)gamma and K(+)K(-)pi(+)pi(-)eta gamma with the hard photon radiated from the initial state. About 20 000, 4300, 5500, and 375 fully reconstructed events, respectively, are 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 the obtained cross sections from the threshold to about 5 GeV can be compared with corresponding direct e(+)e(-) measurements, currently available only for the eta pi(+)pi(-) and omega pi(+)pi(-) submodes of the e(+)e(-)-> 2(pi(+)pi(-))pi(0) channel. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from e(+)e(-)->omega(782)pi(+)pi(-) and study the omega(1420) and omega(1650) resonances. In the charmonium region, we observe the J/psi in all these final states and several intermediate states, as well as the psi(2S) in some modes, and we measure the corresponding branching fractions.