Understanding B -->J/\Psi \phi in the Standard Model

The rare decay $\bar B_d^0\to J/\psi \phi$ can proceed in four distinct mechanisms: (i) production of the $\phi$ via tri-gluon fusion, (ii) photoproduction of the $J/\psi$ or $\phi$, (iii) final-state rescattering of $D_s^{(*)}D_s^{(*)}$ produced in the $\bar B_d$ decay to $J/\psi\phi$, and (iv) production of the $\phi$ via $\omega-\phi$ mixing. In this work, we examine the contributions from photoproduction and final-state rescattering to $\bar B_d^0\to J/\psi \phi$ and find that the corresponding branching ratios are of order $10^{-11}$ and $10^{-9}$, respectively. Hence, this decay is dominated by the $\omega-\phi$ mixing effect.