The role of $D_{(s)}^{\ast }$ and their contributions in $B_{(s)}\to D_{(s)}h{h}^{\prime }$ decays

Abstract

We demonstrate the roles of $D_{(s)}^{\ast }$ and their contributions in the quasi-two-body decays $B_{(s)}\to D_{(s)}h{h}^{\prime }$ ($h,h^{\prime }=\{\pi ,K\}$) in the perturbative QCD approach, stemming from the quark flavour changing $\bar{b}\to \bar{c}{q}_2{\bar{q}}_1$ and $\bar{b}\to c\overline{q_1}\overline{q_2}$ with $q_1,q_2=\{s/d,u\}$. The main motivation of this study is the measurements of significant derivations from the simple phase-space model in the channels $B_{(s)}\to D_{(s)}h{h}^{\prime }$ at $B$ factories and LHC, which is now clarified as the Breit-Wigner-tail effects from the corresponding intermediate resonant states $D_{(s)}^{\ast }$. We confirm that these effect from $D^{\ast }$ is small ($\sim 5\%$) in the quasi-two-body $B_{(s)}\to D\pi \pi (K)$ decaying channels, and predict the tiny ($<1\%$) contributions from $D^{\ast }$ in the $B_{(s)}\to D_{s}K\pi (K)$ decaying channels, our result for the $B_s\to DK\pi (K)$ decaying channels contributed only from the Breit-Wigner-tail effect of $D_s^{\ast }$ is in agreement with the current LHCb measurement. We recommend the Belle-II and the LHCb collaborations to restudy the processes $B^{+}\to {\bar{D}}^{\ast 0}{\pi }^{+}(K^{+})\to D^{-}{\pi }^{+}{\pi }^{+}(K^{+})$ to reveal the structure of $D^{\ast 0}$ and the strong decay $D^{\ast 0}\to D^{+}{\pi }^{-}$.

Comments: 24 pages, 3 figures, 6 tables, minor correction, typos removed