Cross Sections for the Reactions e+e- -> K+ K- pi+pi-, K+ K- pi0pi0, and K+ K- K+ K- Measured Using Initial-State Radiation

We study the processes e{sup +}e{sup -} {yields} K{sup +}K{sup -}{pi}{sup +}{pi}-{gamma}, K{sup +}K{sup -}{pi}{sup 0}{pi}{sup 0}{gamma}, and K{sup +}K{sup -}K{sup +}K{sup -}{gamma}, where the photon is radiated from the initial state. About 84000, 8000, and 4200 fully reconstructed events, respectively, are selected from 454 fb{sup -1} of BABAR data. The invariant mass of the hadronic final state defines the e{sup +}e{sup -} center-of-mass energy, so that the K{sup +}K{sup -}{pi}{sup +}{pi}{sup -}{gamma} data can be compared with direct measurements of the e{sup +}e{sup -} {yields} K{sup +}K{sup -}{pi}{sup +}{pi}{sup -} reaction. No direct measurements exist for the e{sup +}e{sup -} {yields} K{sup +}K{sup -}{pi}{sup 0}{pi}{sup 0} or e{sup +}e{sup -} {yields} K{sup +}K{sup -}K{sup +}K{sup -} reactions, and we present an update of our previous result with doubled statistics. 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{sup +}e{sup -} {yields} {phi}(1020){pi}{pi}{gamma} reaction, and confirm the presence of the Y (2175) resonance in the {phi}(1020)f{sub 0}(980) and K{sup +}K{sup -} f{sub 0}(980) modes. In the charmonium region, we observe the J/{psi} in all three final states andmore » in several intermediate states, as well as the {phi}(2S) in some modes, and measure the corresponding branching fractions.« less