Cross sections for the reactions e(+)e(-) -> K+K-pi(+)pi(-), K+K-pi(0)pi(0), and K+K-K+K- measured using initial-state radiation events

We study the processes e(+)e(-) -> K+K-pi(+)pi(-)gamma, K+K-pi(0)pi(0)gamma, and K+K-K+K-gamma, where the photon is radiated from the initial state. About 84000, 8000, and 4200 fully reconstructed events, respectively, are selected from 454 fb(-1) of BABAR data. The invariantmass of the hadronic final state defines the e(+)e(-) center-of- mass energy, so that the K+K-pi(+)pi(-)gamma data can be compared with direct measurements of the e(+)e(-) -> K+K-pi(+)pi(-) reaction. No directmeasurements exist for the e(+)e(-) -> K+K-pi(0)pi(0) or e(+)e(-) -> K+K-K+K- reactions, andwe present an update of our previous result based on a data sample that is twice as large. Studying the structure of these events, we find contributions froma number of intermediate states and extract their cross sections. In particular, we perform a more detailed study of the e(+)e(-) -> phi(1020)pi pi gamma reaction and confirm the presence of the Y(2175) resonance in the phi(1020)integral(0)(980) and K+K-integral(0)(980) modes. In the charmonium region, we observe the J/psi in all three final states and in several intermediate states, as well as the psi(2S) in some modes, and measure the corresponding products of branching fraction and electron width.