Study of nonleptonic $B_q^{\ast }$ $\to$ $D_{q}V$ and $P_q{D}^{\ast }$ weak decays

Abstract

Motivated by the powerful capability of measurement for the $b$-flavored hadron rare decays at LHC and SuperKEKB/Belle-II, the nonleptonic ${\bar{B}}^{\ast }$ $\to$ $D{\bar{D}}^{\ast }$, $D\ddot{I}{}^{-}$, $D{K}^{\ast -}$, $\ddot{I}€D^{\ast }$ and $K{D}^{\ast }$ weak decays are studied in detail. With the amplitudes calculated with factorization approach and the form factors of $B^{\ast }$ transition into pseudoscalar meson evaluated with the BSW model, branching fractions and polarization fractions are firstly presented. Numerically, the CKM-favored ${\bar{B}}_q^{\ast }$ $\to$ $D_q{D}_s^{\ast -}$ and $D_q\ddot{I}{}^{-}$ decays have large branching fractions, $\sim$ $10^{-8}$, which should be sought for with priority and firstly observed by LHC and Belle-II experiments. The ${\bar{B}}_q^{\ast }$ $\to$ $D_q{K}^{\ast }$ and $D_q\ddot{I}$ decays are dominated by the longitudinal polarization states. While, the parallel polarization fractions of ${\bar{B}}_q^{\ast }$ $\to$ $D_q{\bar{D}}^{\ast }$ decays are comparable with the longitudinal ones, numerically, $f_{\parallel }$ $+$ $f_L$ $\simeq$ 95\% and $f_L:f_{\parallel }$ $\simeq$ $5:4$. Some comparisons between ${\bar{B}}_q^{\ast 0}$ $\to$ $D_{q}V$ and their corresponding ${\bar{B}}_q^0$ $\to$ $D_q^{\ast }V$ decays are performed, and the relation $f_{L,\parallel }({\bar{B}}^{\ast 0}\to DV)\simeq f_{L,\parallel }({\bar{B}}^0\to D^{\ast +}{V}^{-})$ is presented. Besides, with the implication of $SU(3)$ flavor symmetry, some useful ratios $R_{\mathrm{du}}$ and $R_{\mathrm{ds}}$ are discussed in detail, and suggested to be verified experimentally.

15 pages, 3 tables; the version published in Adv. High Energy Phys