The $ρ(770,1450)\to ωπ$ contributions for three-body decays $B\to\bar{D}^{(*)} ωπ$

Abstract

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