Quasi-two-body decays $B\to P f_0(500)\to P\pi^+\pi^-$ in the perturbative QCD approach

TL;DR

This paper investigates quasi-two-body B meson decays involving the $f_0(500)$ scalar meson using perturbative QCD, calculating branching fractions and CP asymmetries with predictions testable by experiments.

Contribution

It provides the first detailed PQCD calculation of $B o P f_0(500) o P\pi^+\pi^-$ decays, including differential distributions and CP violation effects.

Findings

Total branching fraction: (1.78 ± 0.41 ± 0.51) × 10^{-6}

Direct CP violation: (29.8 ± 11.1 ± 13.0)%

Results are consistent with current experimental data and predictions.

Abstract

In this paper, we study the quasi-two-body decays $B\to P f_0(500)\to P\pi^+\pi^-$ [with $P=(\pi, K, \eta, \eta^{\prime})$] within framework of perturbative QCD (PQCD) factorization approach. With the help of $\pi$-$\pi$ distribution amplitude and scalar form factor $F_{\pi\pi}(\omega^2)$, we calculate the $CP$ averaged branching fraction and the $CP$ asymmetry for the quasi-two-body decays $B\to P f_0(500)\to P\pi^+\pi^-$. Taking the quasi-two-body decay $B^+ \to \pi^+ f_0(500) \to \pi^+ \pi^+ \pi^-$ as an explicit example, we present the behavior of differential branching fraction and direct $CP$ violation versus the $\pi$-$\pi$ invariant mass. The total branching fraction and direct $CP$ violation are $\mathcal{B}(B^+\to \pi^+ [\sigma\to]\pi^+\pi^-) = (1.78 \pm 0.41\pm 0.51) \times 10^{-6}$ and $\mathcal{A}_{CP}(B^+\to \pi^+ [\sigma\to]\pi^+\pi^-) = (29.8\pm 11.1\pm 13.0)\%$ respectively. Our results could be tested by further experiments.