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In this work, we present an analysis of the nonleptonic charmonium modes$B_s^0 \to J / \psi f_2^\prime(1525)$ and $B_s^0 \to J/\psi K^+K^-$. Within theframework of the factorization approach and using the perturbative QCD for theevaluation of the relevant form factors, we find a branching fraction for thetwo-body channel of BR$(B_s^{0} \to J/\psi f_2^{\prime}(1525)) = (1.6{}^{+0.9}_{-0.7})\times 10^{-4}$ which is in agreement with the experimentalvalues reported by the LHCb and Belle Collaborations. The associatedpolarization fractions to this vector-tensor mode are also presented. On theother hand, non-resonant and resonant contributions to the three-body decay$B_s^0 \to J/\psi K^+K^-$ are carefully investigated. The dominantcontributions of the resonances $ \phi(1020)$ and $f_2^{\prime}(1525)$ areproperly taken into account. A detailed analysis of the $K^+ K^-$ invariantmass distributions and Dalitz plot are also performed. The overall resultBR$(B_s^{0} \to J/\psi K^+ K^-) = (9.3^{+1.3}_{-1.1})\times 10^{-4}$ is also insatisfactory agreement with the experimental information reported by LHCb andBelle.

Analysis of the nonleptonic charmonium modes $B_s^0 \to J/\psi f_{2}^{\prime}(1525)$ and $B_s^0 \to J/\psi K^+K^-$