Quasi-two-body decays $B_c\to D^{\ast }h\to D\pi h$ in the perturbative QCD

Abstract

In this work, we investigate the quasi-two-body decays $B_c\to D^{\ast }h\to D\pi h$ with $h=(K^0,{\pi }^0,\eta ,{\eta }^{\prime })$ using the perturbative QCD(PQCD) approach. The description of final state interactions between the $D\pi$ pair is achieved through the two-meson distribution amplitudes(DAs), which are normalized to the time-like form factor. The PQCD predictions on the branching ratios of the quasi-two-body decays $B_c\to D^{\ast }h\to D\pi h$ show an obvious hierarchy: $Br(B_c^{+}\to D^{\ast +}{K}^0\to D^0{\pi }^{+}{K}^0)=({5.22}_{-0.74}^{+0.86})\times {10}^{-6},Br(B_c^{+}\to D^{\ast +}{\pi }^0\to D^0{\pi }^{+}{\pi }^0)=(0.93\pm 0.26)\times {10}^{-7},Br(B_c^{+}\to D^{\ast +}\eta \to D^0{\pi }^{+}\eta )=({2.83}_{-0.52}^{+0.59})\times {10}^{-8}$ and $Br(B_c^{+}\to D^{\ast +}{\eta }^{\prime }\to D^0{\pi }^{+}{\eta }^{\prime })=({1.89}_{-0.36}^{+0.40})\times {10}^{-8}$. From the invariant mass $m_{D\pi }$-dependence of the decay spectrum for each channel, one can find that the branching fraction is concentrated in a narrow region around the $D^{\ast }$ pole mass. So one can obtain the branching ratios for the corresponding two-body decays $B_c\to D^{\ast +}h$ under the narrow width approximation. We find that the branching ratios of the decays $B_c\to D^{\ast +}h$ are consistent well with the previous PQCD calculations within errors. These predictions will be tested by the future experiments.

Comments: 12 pages, 3 figures, accepted for publication in Chin. Phys. C