$J/\psi \to D_{s,d}\pi$, $D_{s,d}K$ decays with perturbative QCD approach

Besides the conventional strong and electromagnetic decay modes, the $J/\psi$ particle can also decay via the weak interaction in the standard model. In this paper, nonleptonic $J/\psi \to D_{s,d}\pi$, $D_{s,d}K$ weak decays, corresponding to the externally emitted virtual $W$ boson process, are investigated with the perturbative QCD approach. It is found that the branching ratio for the Cabibbo-favored $J/\psi \to D_s\pi$ decay can reach up to $\mathcal{O}({10}^{-10})$, which might be potentially measurable at the future high-luminosity experiments.

Figure 1

The shape lines of wave functions for the $J/\psi$ meson in (a) and the $D_{d,s}$ mesons in (b), where the expressions of ${\varphi }_{\psi }^{v,t}(x)$, ${\varphi }_D^{a,p}(x)$, and ${\varphi }_D(x,b)$ are given in Eqs. (30), (31), (32), (33), and (35).

Figure 2

Feynman diagrams for the $J/\psi \to D_s\pi$ decay, where (a) and (b) are factorizable emission diagrams; (c) and (d) are nonfactorizable emission diagrams.

Figure 3

Contributions to form factor $A_0^{J/\psi \to D_s}$ in (a) and branching ratio $\mathcal{B}r(J/\psi \to D_s\pi )$ in (b) from different regions of ${\alpha }_s/\pi$ (horizontal axes), where the numbers over the histograms denote the percentages of the corresponding contributions.