Abstract
We study the contributions for the K^+K^- and K^0bar{K}^0 originating from the intermediate states phi (1020) and phi (1680) in the charmless three-body decays Brightarrow Kbar{K} h, with h=(pi , K), in the perturbative QCD approach. The subprocesses phi (1020,1680)rightarrow Kbar{K} are introduced into the distribution amplitudes of Kbar{K} system via the kaon electromagnetic form factors with the coefficients taken from the fitted results. The predictions of the branching fractions for the decays Brightarrow phi (1680)h with the intermediate state phi (1680) decays into K^+K^- or K^0bar{K}^0 are about 6{-}8% of the corresponding results for the quasi-two-body decays Brightarrow phi (1020)h rightarrow K^+ K^- h in this work.
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