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