Resonant state $D_0^{\ast }(2400)$ in the quasi-two-body $B$ meson decays

Abstract

We study four quasi-two-body decay processes including $D_0^{\ast }(2400)$ as the intermediate state in perturbative QCD (PQCD) approach. The branching fraction predicted in this work for the decay mode $B^{-}\to D_0^{\ast }(2400{)}^0{\pi }^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ agree with the data from Belle, BaBar and LHCb Collaborations. The PQCD prediction of the branching ratio for the decay ${\bar{B}}^0\to D_0^{\ast +}{K}^{-}\to D^0{\pi }^{+}{K}^{-}$ is consistent with the value given by LHCb. For the decays ${\bar{B}}^0\to D_0^{\ast +}{\pi }^{-}\to D^0{\pi }^{+}{\pi }^{-}$ and $B^{-}\to D_0^{\ast 0}{K}^{-}\to D^{+}{\pi }^{-}{K}^{-}$, the PQCD predicted branch ratios are $2.85_{-0.80}^{+1.23}({\omega }_B{)}_{-0.81}^{+1.05}({\omega }_{D\pi }{)}_{-0.31}^{+0.33}(a_{D\pi }{)}_{-0.05}^{+0.06}({\Gamma }_{D_0^{\ast +}})\times 10^{-4}$ and $4.65_{-1.30}^{+1.89}({\omega }_B{)}_{-1.24}^{+1.51}({\omega }_{D\pi }{)}_{-0.38}^{+0.40}(a_{D\pi }{)}_{-0.18}^{+0.22}({\Gamma }_{D_0^{\ast 0}})\times 10^{-5}$, respectively. We analyze the experimental branching fractions using the ratios $R_{D_0^{\ast 0}}$ and $R_{D_0^{\ast +}}$ which are related to the decays with the neutral and charged $D_0^{\ast }(2400)$, respectively. The available experimental results for the quasi-two-body decays including $D_0^{\ast }(2400)$ are not in agreement with the isospin relation and $SU(3)$ flavor symmetry.

Comments: 9 pages, 3 figures; Version submitted to Physics Letters B