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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.02419 |
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Table of Contents:
- In this paper, we study the quasi-two-body decays $B\to P f_0(500)\to Pπ^+π^-$ [with $P=(π, K, η, η^{\prime})$] within framework of perturbative QCD (PQCD) factorization approach. With the help of $π$-$π$ distribution amplitude and scalar form factor $F_{ππ}(ω^2)$, we calculate the $CP$ averaged branching fraction and the $CP$ asymmetry for the quasi-two-body decays $B\to P f_0(500)\to Pπ^+π^-$. Taking the quasi-two-body decay $B^+ \to π^+ f_0(500) \to π^+ π^+ π^-$ as an explicit example, we present the behavior of differential branching fraction and direct $CP$ violation versus the $π$-$π$ invariant mass. The total branching fraction and direct $CP$ violation are $\mathcal{B}(B^+\to π^+ [σ\to]π^+π^-) = (1.78 \pm 0.41\pm 0.51) \times 10^{-6}$ and $\mathcal{A}_{CP}(B^+\to π^+ [σ\to]π^+π^-) = (29.8\pm 11.1\pm 13.0)\%$ respectively. Our results could be tested by further experiments.