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In 2017, LHCb collaboration reported their first observation of the raredecays $B_s \to \phi (f_0(980)$ $/f_2(1270) \to ) \pi^+\pi^-$ and the evidenceof $B^0 \to \phi(f_0(980)/f_2(1270)\to)\pi^+\pi^-$. Motivated by this, we studythese quasi-two-body decays in the perturbative QCD approach. The branchingfractions, $CP$ asymmetries and the polarization fractions are calculated. Wefind that within the appropriate two-meson wave functions, the calculatedbranching fractions are in agreement with the measurements of LHCb. Based onthe narrow-width approximation, We also calculate the branching fractions ofthe quasi-two-body $B_{d,s}\to \phi(f_0(980)/f_2(1270)\to) \pi^0\pi^0$ and$B_{d,s}\to \phi(f_2(1270)\to) K^+K^-$, and hope the predictions to be testedin the ongoing LHCb and Belle II experiments. Moreover, the processes$B_{d,s}\to \phi f_2(1270)$ are also analyzed under this approximation. We notethat the $CP$ asymmetries of these decays are very small, because these decaysare either penguin dominant or pure penguin processes.

Study of Quasi-two-body $B_{(s)}\to \phi (f_0(980)/f_2(1270)\to)\pi\pi$ Decays in Perturbative QCD Approach