The ρ(770, 1450) → ωπ contributions for three-body decays $$ B\to {\overline{D}}^{\left(\ast \right)}\omega \pi $$

Abstract

Abstract The decays $$ B\to {\overline{D}}^{\left(\ast \right)}\omega \pi $$ B → D ¯ ∗ ωπ are very important for the investigation of ρ excitations and the test of factorization hypothesis for B meson decays. The $$ {B}^{+}\to {\overline{D}}^{\left(\ast \right)0}\omega {\pi}^{+} $$ B + → D ¯ ∗ 0 ω π + and B0 → 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) → ωπ for the cascade decays $$ {B}^{+}\to {\overline{D}}^{\left(\ast \right)0}{\rho}^{+}\to {\overline{D}}^{\left(\ast \right)0}\omega {\pi}^{+} $$ B + → D ¯ ∗ 0 ρ + → D ¯ ∗ 0 ω π + , B0 → D(*)−ρ+ → D(*)−ωπ+ and $$ {B}_s^0\to {D}_s^{\left(\ast \right)-}{\rho}^{+}\to {D}^{\left(\ast \right)-}\omega {\pi}^{+} $$ B s 0 → D s ∗ − ρ + → D ∗ − ω π + . We introduce ρ(770, 1450) → ωπ subprocesses into the distribution amplitudes for ωπ system via the vector form factor Fωπ(s) and then predict the branching fractions for the first time for concerned quasi-two-body decays with ρ(770, 1450) → ωπ, as well as the corresponding longitudinal polarization fractions ΓL/Γ for the cases with the vector $$ {\overline{D}}^{\ast 0} $$ D ¯ ∗ 0 or $$ {D}_{(s)}^{\ast -} $$ 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 B0 → D*−ρ(770)+ → D*−ωπ+ and B0 → D*−ρ(1450)+ → 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 $$ {B}_s^0\to {D}_s^{\ast -}\rho {\left(770,1450\right)}^{+} $$ B s 0 → D s ∗ − ρ 770 1450 + decays, which have only emission diagrams at quark level, to test the factorization hypothesis for B decays.