The $\epem\toπ^+π^-π^+π^-$, $K^+K^-π^+π^-$, and $K^+K^- K^+K^- $ Cross Sections at Center-of-Mass Energies 0.5--4.5 \gev Measured with Initial-State Radiation

Abstract

We study the process $e^+e^-\toπ^+π^-π^+π^-γ$, with a hard photon radiated from the initial state. About 60,000 fully reconstructed events have been selected from 89 $fb^{-1}$ of BaBar data. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy, so that these data can be compared with the corresponding direct $e^+e^-$ measurements. From the $4π$-mass spectrum, the cross section for the process $e^+e^-\toπ^+π^-π^+π^-$ is measured for center-of-mass energies from 0.6 to 4.5 $GeV/c^2$. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states $K^+ K^- π^+π^-$ and $K^+ K^- K^+ K^-$. We observe the $J/ψ$ in all three final states and measure the corresponding branching fractions. We search for X(3872) in $J/ψ(\toμ^+μ^-) π^+π^-$ and obtain an upper limit on the product of the $e^+e^-$ width of the X(3872) and the branching fraction for $X(3872) \to J/ψπ^+π^-$.