Quasi-two-body decays B_cD*hDh in perturbative QCD

In this work, we investigate the quasi-two-body decays B-c -> D*h -> D pi h with h = (K-0, pi(0), eta, eta') using the perturbative QCD (PQCD) approach. The description of final state interactions of 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 -> D*h -> D pi h show an obvious hierarchy: and.Br (B-c(+) -> D*(+) K-0 -> D-0 pi(+) K-0) = (5.22(-0.74)(+0.86)) x 10(-6) , Br(B-c(+) -> D*(+) pi(0) -> D-0 pi(+) pi(0)) = (0.93 +/- 0.26) x 10(-7) , Br(B-c(+) -> D*(+)eta -> D-0 pi(+) eta) = (2.83(-0.52)(+0.59)) x 10(-8) and Br(B-c(+) -> D*(+) eta' -> D-0 pi(+) eta') = (1.89(-0.36)(+0.40)) From the invariant mass -dependence of the decay spectrum for each channel, one can find that the branching fraction is concentrated in a narrow region around the D* pole mass. Thus, one can obtain the branching ratios for the corresponding two-body decays B-c -> D*(+)h under the narrow-width approximation. We find that the branching ratios of the decays B-c -> D*(+)h are consistent with the previous PQCD calculations within errors. These predictions will be tested in future experiments.