Study of ${\bar{B}}^0\to D^0{\mu }^{+}{\mu }^{-}$ Decay in Perturbative QCD Approach

Within the perturbative QCD approach and ignoring the contributions of long distance and subleading penguin loops, we investigate $\bar B^0 \to D^0 \mu^+\mu^-$ decay in the large recoiling kinematic region in the Standard Model. At the tree level, ${\bar{B}}^0$ decays to $D^0$ by exchanging a $W$ boson accompanied by a virtual photon emission from the valence quarks of ${\bar{B}}^0$ and $D^0$ meson, then the virtual photon decays to the lepton pair. Numerically, we find that the branching ratio decreases rapidly as the $q^2$ increases, and the branching ratio of ${\bar{B}}^0\to D^0{\mu }^{+}{\mu }^{-}$ is $(9.7_{-3.2}^{+4.2})\times {10}^{-6}$ in the region $q^2 \in [1,5] $\mathrm{G}\mathrm{e}\mathrm{V}$^2$. The order of the branching ratio shows a possibility to study this interesting channel in the current $B$ factories and the Large Hadron Collider. The precise experimental data will help us to test the factorization approach and the QCD theory, in general.