e+e−→π+π−π+π−,K+K−π+π−, andK+K−K+K−cross sections at center-of-mass energies 0.5–4.5 GeV measured with initial-state radiation

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Abstract

We study the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$, with a hard photon radiated from the initial state. About 60 000 fully reconstructed events have been selected from $89\text{ }\text{ }{\mathrm{f}\mathrm{b}}^{\ensuremath{-}1}$ of BABAR data. The invariant mass of the hadronic final state defines the effective ${e}^{+}{e}^{\ensuremath{-}}$ ${e}^{+}{e}^{\ensuremath{-}}$ center-of-mass energy, so that these data can be compared with the corresponding direct ${e}^{+}{e}^{\ensuremath{-}}$ measurements. From the $4\ensuremath{\pi}$ -mass spectrum, the cross section for the process ${e}^{+}{e}^{\ensuremath{-}}$ $\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is measured for center-of-mass energies from 0.6 to 4.5 $\mathrm{G}\mathrm{e}\mathrm{V}$. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states ${K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{+}{K}^{\ensuremath{-}}{K}^{+}{K}^{\ensuremath{-}}$. We observe the $J/\ensuremath{\psi}$ in all three final states and measure the corresponding branching fractions. We search for $X(3872)$ in $J/\ensuremath{\psi}(\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and obtain an upper limit on the product of the ${e}^{+}{e}^{\ensuremath{-}}$ width of the $X(3872)$ and the branching fraction for $X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$.

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