Study of ${\bar{B}^0} \to {D^0}{\mu^{+} }{\mu^{-} }$ decay in perturbative QCD approach

Abstract

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 $\left( {9.7_{ - 3.2}^{ + 4.2}} \right) \times {10^{ - 6}}$ in the region q ² ∈ [1, 5] GeV². 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.