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−π+π−γ, K+K−π0π0γ, and K+K−K+K−γ, where the photon is radiated from the initial state. About 84 000, 8000, and 4200 fully reconstructed events, respectively, are selected from 454  fb−1 of BABAR data. The invariant mass of the hadronic final state defines the e+e− center-of-mass energy, so that the K+K−π+π−γ data can be compared with direct measurements of the e+e−→K+K−π+π− reaction. No direct measurements exist for the e+e−→K+K−π0π0 or e+e−→K+K−K+K− reactions, and we 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 from a number of intermediate states and extract their cross sections. In particular, we perform a more detailed study of the e+e−→ϕ(1020)ππγ reaction and confirm the presence of the Y(2175) resonance in the ϕ(1020)f0(980) and K+K−f0(980) modes. In the charmonium region, we observe the J/ψ in all three final states and in several intermediate states, as well as the ψ(2S) in some modes, and measure the corresponding products of branching fraction and electron width.