Subprocesses $\rho (770,1450)\to K\bar{K}$ for the three-body hadronic $D$ meson decays

Abstract

We construct the theoretical framework for quasi-two-body $D$ meson decays with the help of pion and kaon electromagnetic form factors, and with which we study the contributions of the subprocesses $\rho (770,1450)\to K\bar{K}$ for the three-body $D$ decays within the flavour $SU(3)$ symmetry. Because of the limitations imposed by phase space and strong coupling, the contributions for kaon pair from the virtual bound state $\rho (770)$ are channel-dependent and generally small for the concerned three-body $D$ decays. But some quasi-two-body processes could still be observed in the Dalitz plot analyses for related decays, such as $D^0\to K^{-}\rho (770{)}^{+}\to K^{-}{K}^{+}{K}_S^0$ and $D^{+}\to K_S^0\rho (770{)}^{+}\to K_S^0{K}^{+}{K}_S^0$, they are predicted to have the branching fractions $\mathcal{B}=(0.82\pm 0.04)\times 10^{-4}$ and $\mathcal{B}=0.47_{-0.03}^{+0.05}\times 10^{-4}$, which are $(1.86\pm 0.16)\%$ and $(1.84_{-0.16}^{+0.21})\%$, respectively, of the total branching fractions for the corresponding three-body $D$ decays. We find in this work that the normal subprocesses like $\rho (1450{)}^{+}\to {\pi }^{+}{\pi }^0$ or $\rho (1450{)}^{+}\to K^{+}{\bar{K}}^0$, which are bound by the masses of decaying initial states, will provide virtual contributions in some special decays.

Comments: 10 pages, 3 figures, accepted for publication in Phys.Rev.D