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In this work, we make a detailed analysis on the penguin-dominant processes$B_{(s)}^0 \to \phi\phi \to (K^+K^-)(K^+K^-)$ in the perturbative QCD (PQCD)approach. In addition to the dominant $P$-wave resonance, the scalar background$f_0(980) \to K^+K^-$ is also accounted for. We improve the Gegenbauer momentsin $KK$ two-meson distribution amplitudes by fitting the PQCD factorizationformulas to measured branching ratios of three-body and four-body $B$ decays.We extract the branching ratios of two-body $B_{(s)}^0 \to \phi\phi$ decaysfrom the corresponding four-body decay modes and calculate the relevantpolarization fractions together with two relative phases$\phi_{\parallel,\perp}$, which are consistent with the previous theoreticalpredictions. The PQCD predictions for the "true" triple product asymmetries(TPAs) are zero which are expected in the standard model due to the vanishingweak phase difference, and support the current data reported by the CDF andLHCb Collaborations. A large "fake" TPA $\mathcal{A}_\text{T-fake}^1=30.4\%$ ofthe decay $B^0_s \to \phi\phi \to (K^+K^-)(K^+K^-)$ is predicted for the firsttime, which indicates the presence of the significant final-state interactions.The TPAs of the rare decay channel $B^0 \to \phi\phi\to (K^+K^-)(K^+K^-)$ arealso predicted and can be tested in the near future.

Study of $B_{(s)}^0 \to \phi\phi \to (K^+K^-)(K^+K^-)$ decays in the perturbative QCD approach