Two- and three-body hadronic decays of charmed mesons involving a tensor meson

Abstract

We study the quasi-two-body $D\ensuremath{\rightarrow}TP$ decays and the three-body $D$ decays proceeding through intermediate tensor resonances, where $T$ and $P$ denote tensor and pseudoscalar mesons, respectively. We employ the $D\ensuremath{\rightarrow}T$ transition form factors based upon light cone sum rules and the covariant light-front quark model to evaluate the decay rates, with the former giving a better agreement with current data. Though the tree amplitudes with the emitted meson being a tensor meson vanish under factorization approximation, contributions proportional to the tensor decay constant ${f}_{T}$ can be produced from vertex and hard spectator-scattering corrections. We also investigate the finite-width effects of the tensor mesons and find that, contrary to three-body $B$ decays, the tensor-mediated $D$ decays are more seriously affected and the narrow width approximation has to be corrected. More experimental data are required in order to extract information topological amplitudes associated with quasi-two-body $D\ensuremath{\rightarrow}TP$ decays. Among the data, the ${D}^{+}\ensuremath{\rightarrow}{f}_{2}{\ensuremath{\pi}}^{+}$ and ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}_{2}^{*0}{\ensuremath{\pi}}^{+}$ branching fractions are not self-consistent and further clarification is called for.