The e+ e- ---> K+ K- pi+ pi-, K+ K- pi0 pi0 and K+ K- K+ K- cross-sections measured with initial-state radiation

, where the photon is radiated from the initial state. About 34600, 4400 and 2300 fully reconstructed events, respectively, are selected from 232 \invfb of \babar data. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy, so that the

K^+ K^- \pi^+\pi^-\gamma

data can be compared with direct measurements of the e^+ e^-\to K^+K^- \pipi reaction/ no direct measurements exist for the

e^+ e^-\to K^+ K^- \pi^0\pi^0

or \epem\to K^+ K^- K^+ K^- reactions. 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^-\to\phi(1020) f_{0}(980)

and study its structure near threshold. In the charmonium region, we observe the

J/\psi

in all three final states and several intermediate states, as well as the

\psi(2S)

in some modes, and measure the corresponding branching fractions. We see no signal for the Y(4260) and obtain an upper limit of \BR_{Y(4260)\to\phi\pi^+\pi^-}\cdot\Gamma^{Y}_{ee}<0.4 \ev at 90% C.L.

13.25.Jx
14.40.Cs
13.25.Gv
13.66.Bc
electron positron: colliding beams
electron positron: annihilation
hadron: multiple production
mass spectrum: (2K+ 2K-)
mass spectrum: (K+ K- 2pi)
radiation: initial-state interaction

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