| Abstract |
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We study the processes $\e^+e^-\!\rightarrow 2(\pi^+\pi^-)\pi^0\gamma$,
$2(\pi^+\pi^-)\eta\gamma$, $K^+K^-\pi^+\pi^-\pi^0\gamma$ and
$K^+K^-\pi^+\pi^-\eta\gamma$ with the hard photon radiated from the
initial state. About 20000, 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
$\e^+e^-\!\rightarrow 2(\pi^+\pi^-)\pi^0$ 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
$\e^+e^-\!\rightarrow\omega(782)\pi^+\pi^-$ 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.
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