The e+e-→2(π+π-)π0, 2(π+π-)η, K+K-π+π-π0 and K+K-π+π-η cross sections measured with initial-state radiation

We study the processes e+e-→2(π+π-)π0γ, 2(π+π-)ηγ, K+K-π+π-π0γ and K+K-π+π-ηγ 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 ηπ+π- and ωπ+π- submodes of the e+e-→2(π+π-)π0 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-→ω(782)π+π- and study the ω(1420) and ω(1650) resonances. In the charmonium region, we observe the J/ψ in all these final states and several intermediate states, as well as the ψ(2S) in some modes, and we measure the corresponding branching fractions.