The $\rho (770,1450)\to \omega \pi$ contributions for three-body decays $B\to {\bar{D}}^{(\ast )}\omega \pi$

Abstract

The decays $B\to {\bar{D}}^{(\ast )}\omega \pi$ are very important for the investigation of $\rho$ excitations and the test of factorization hypothesis for $B$ meson decays. The $B^{+}\to {\bar{D}}^{(\ast )0}\omega {\pi }^{+}$ and $B^0\to D^{(\ast )-}\omega {\pi }^{+}$ have been measured by different collaborations but without any predictions for their observables on theoretical side. In this work, we study the contributions of $\rho (770,1450)\to \omega \pi$ for the cascade decays $B^{+}\to {\bar{D}}^{(\ast )0}{\rho }^{+}\to {\bar{D}}^{(\ast )0}\omega {\pi }^{+}$, $B^0\to D^{(\ast )-}{\rho }^{+}\to D^{(\ast )-}\omega {\pi }^{+}$ and $B_s^0\to D_s^{(\ast )-}{\rho }^{+}\to D^{(\ast )-}\omega {\pi }^{+}$. We introduce $\rho (770,1450)\to \omega \pi$ subprocesses into the distribution amplitudes for $\omega \pi$ system via the vector form factor $F_{\omega \pi }(s)$ and then predict the branching fractions for the first time for concerned quasi-two-body decays with $\rho (770,1450)\to \omega \pi$, as well as the corresponding longitudinal polarization fractions ${\Gamma }_L/\Gamma$ for the cases with the vector ${\bar{D}}^{\ast 0}$ or $D_{(s)}^{\ast -}$ in their final states. The branching fractions of these quasi-two-body decays are predicted at the order of $10^{-3}$, which can be detected at the LHCb and Belle-II experiments. The predictions for the decays $B^0\to D^{\ast -}\rho (770{)}^{+}\to D^{\ast -}\omega {\pi }^{+}$ and $B^0\to D^{\ast -}\rho (1450{)}^{+}\to D^{\ast -}\omega {\pi }^{+}$ agree well with the measurements from Belle Collaboration. In order to avoid the pollution from annihilation Feynman diagrams, we recommend to take the $B_s^0\to D_s^{\ast -}\rho (770,1450{)}^{+}$ decays, which have only emission diagrams at quark level, to test the factorization hypothesis for $B$ decays.

arXiv comment30 pages, 4 figures, the typos in Eq.(2.33) were corrected

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Cited by in corpus (3)

• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• Contributions of $\rho (770,1450)\to \omega \pi$ for the Cabibbo-favored $D\to h\omega \pi$ decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays