Quasi-two-body decays B_(c)→D^(*)h→Dπh in perturbative QCD

In this work,we investigate the quasi-two-body decays B_(c)→D^(*)h→Dπhwithh=(K^(0),π^(0),η,η′)using the perturbative QCD(PQCD)approach.The description of final state interactions of the Dπpair 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→Dπh show an obvious hierarchy:Br(B^(+)_(c)→D^(∗+)K^(0)→D^(0)π^(+)K^(0))=(5.22^(+0.86)_(-0.74))×10^(-6),Br(B^(+)_(c)→D^(∗+)π^(0)→D^(0)π^(+)π^(0))=(0.93±0.26)×10^(-7),Br(B^(+)_(c)→D^(∗+)η→D^(0)π^(+)η)=(2.83^(+0.59)_(-0.52))×10^(-8)and Br(B^(+)_(c)→D^(∗+)η′→D^(0)π^(+)η′)=(1.89+0.40-0.36)×10^(-8).From the invariant mass m Dπ-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.