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In the present study, the calculations of two-body decays B^{0}_{s}\rightarrow \ TT [ T denotes tensor mesons, a_{2}(1320), K^{*}_{2}(1430),f_{2}(1270), f^{'}_{2}(1525)] in the perturbative QCD approach are presented.The ensuing predictions encompass branching ratios, polarization fractions, anddirect CP violations, all elucidated in comprehensive detail. It is discernedthat (1) for pure annihilation decay, the longitudinal polarization is around90.0\%, whereas the transverse polarizations manifest comparatively diminutivemagnitudes. (2) The direct CP asymmetry is directly proportional to theinterference between the tree and penguin contributions. For most of the decaysinvestigated within this discourse, the direct CP asymmetry remains modest inmagnitude. (3) There are precisely six distinct categories of Feynman diagramsfor B^{0}_{s} \rightarrow \ TT , because the tensor mesons cannot be producedthrough the (V \pm A) currents or (S \pm P) density, thereby prohibitingfactorizable emission diagrams. The nonfactorizable and annihilationcontributions are ascertained to be pivotal in these decay modes. Thecalculated branching ratios of our calculation for B^{0}_{s} \rightarrow \ TTare at the order of 10^{-6} and 10^{-7}, which can be tested in the LHCb andBelle II experiments. (4) Mixing exists for the f_{2}(1270) andf^{'}_{2}(1525), just as the \eta and \eta^{'} mixing, the branching ratiosabout the mixing angle \theta are given in this work. However, it is differentfrom f_{1}(1285)-f_{1}(1420), the mixing angle is notably small, therebyresulting in only marginal alterations in the decay branching ratios.

Study of B^{0}_{s} \rightarrow \ TT(a_{2}(1320),K^{*}_{2}(1430),f_{2}(1270),f^{'}_{2}(1525)) in the perturbative QCD approach