Subprocesses ρ(770,1450)→KK¯ 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 $\ensuremath{\rho}(770,1450)\ensuremath{\rightarrow}K\overline{K}$ for the three-body $D$ decays within the flavor $SU(3)$ symmetry. Because of the limitations imposed by phase space and strong coupling, the contributions for the kaon pair from the virtual bound state $\ensuremath{\rho}(770)$ 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 ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}\ensuremath{\rho}(770{)}^{+}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}^{+}{K}_{S}^{0}$ and ${D}^{+}\ensuremath{\rightarrow}{K}_{S}^{0}\ensuremath{\rho}(770{)}^{+}\ensuremath{\rightarrow}{K}_{S}^{0}{K}^{+}{K}_{S}^{0}$, they are predicted to have the branching fractions $\mathcal{B}=(0.82\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $\mathcal{B}=0.4{7}_{\ensuremath{-}0.03}^{+0.05}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, which are $(1.86\ifmmode\pm\else\textpm\fi{}0.16)%$ and $(1.8{4}_{\ensuremath{-}0.16}^{+0.21})%$, respectively, of the total branching fractions for the corresponding three-body $D$ decays. We find in this work that the normal subprocesses like $\ensuremath{\rho}(1450{)}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ or $\ensuremath{\rho}(1450{)}^{+}\ensuremath{\rightarrow}{K}^{+}{\overline{K}}^{0}$, which are bound by the masses of decaying initial states, will provide virtual contributions in some special decays.