Analysis of S-wave $ωπ$ dynamics behavior in multi-body B₄ and B₆ decays

The b₁(1235) state has a sizable decay width, which have longstanding puzzle in treating as a final state in theoretical calculations may lead to systematic deviations in the predicted observables. To address this issue and further explore the internal structure of this resonance, we study the multi-body semileptonic decays B₄ and B₆. Within the approximation where the b₁(1235) resonance dominates, we study the B₄ decay B→ b₁(1235)(→ωπ)⁺ν_ in the QCD light-cone sum rules framework. The corresponding transition form factors (TFFs) are calculated by constructing a correlation function with a right-handed chiral current. As the main nonperturbative input for the TFFs calculation, the transverse twist-2 light-cone distribution amplitude (LCDA) of the b₁(1235) resonance is constructed using the light-cone harmonic oscillator model, and the resulting LCDA exhibits a single-peak behavior. At the large-recoil region, we obtain the TFFs V0, 1, 2(0) and $A(0)$, together with the corresponding TFFs ratios rV = 1.530-0.016+0.013 and r₂ = 0.553-0.015+0.012. We then further study the complete B₄ decay by incorporating the b₁(1235)→ωπ resonant line shape and obtain the corresponding observables. The results show that the branching ratio of the B₄ decay is about $1/3$ of that obtained when b₁(1235) is treated as a final state. We also account for the subsequent decay ω→ π⁺π⁻π⁰ and further predicted the branching ratio of the B₆ decay B→ b₁(1235)(→ω(→ π⁺π⁻π⁰)π)⁺ν_. These results may provide useful references for future experimental measurements and further theoretical studies.