Study of the reactions $e^+e^-\to2(\pi^+\pi^-)\pi^0\pi^0\pi^0$ and $e^+e^-\to2(\pi^+\pi^-)\pi^0\pi^0\eta$ at center-of-mass energies from threshold to 4.5 GeV using initial-state radiation

We study the processes $e^+e^-\to 2(\pi^+\pi^-)\pi^0\pi^0\pi^0\gamma$ and $2(\pi^+\pi^-)\pi^0\pi^0\eta\gamma$ in which an energetic photon is radiated from the initial state. The data were collected with the \babar~ detector at SLAC. About 14\,000 and 4700 events, respectively, are selected from a data sample corresponding to an integrated luminosity of 469 fb^{-1}. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy. The center-of-mass energies range from threshold to 4.5 GeV. From the mass spectra, the first ever measurements of the $e^+e^-\to 2(\pi^+\pi^-)\pi^0\pi^0\pi^0$ and the $e^+e^-\to2(\pi^+\pi^-)\pi^0\pi^0\eta$ cross sections are performed. The contributions from $\omega\pi^+\pi^-\pi^0\pi^0$, $\eta2(\pi^+\pi^-)$, and other intermediate states are presented. We observe the $J/\psi$ and $\psi(2S)$ in most of these final states and measure the corresponding branching fractions, many of them for the first time.