$S$-wave resonance contributions to the $B^0_{(s)}\to J/\psi\pi^+\pi^-$ and $B_s\to\pi^+\pi^-\mu^+\mu^-$ decays

TL;DR

This paper investigates the contributions of S-wave resonances to specific B meson decays using perturbative QCD, modeling scalar form factors with resonance parameterizations, and finds results consistent with experimental data.

Contribution

It introduces a novel approach to model S-wave resonance effects in B decays using two-hadron distribution amplitudes within the PQCD framework, including both resonant and nonresonant contributions.

Findings

Branching fractions match experimental data.

Resonant and nonresonant contributions are effectively modeled.

Predictions for CP asymmetries can be made using the derived amplitudes.

Abstract

We study $S$-wave resonance contributions to the $B^0_{(s)}\to J/\psi\pi^+\pi^-$ and $B_s\to\pi^+\pi^-\ell^+\ell^-$ decays in the perturbative QCD (PQCD) framework by introducing two-hadron distribution amplitudes for final states. The Breit-Wigner formula for the $f_0(500)$, $f_0(1500)$ and $f_0(1790)$ resonances and the Flatt\'e model for the $f_0(980)$ resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes, which include both resonant and nonresonant contributions. The resultant branching fraction and differential branching fraction in the pion-pair invariant mass for each resonance channel are consistent with experimental data. The determined $S$-wave two-pion distribution amplitudes, containing the information of both resonant and nonresonant rescattering phases, can be employed to predict direct CP asymmetries of other three-body hadronic $B$ meson decays in various localized regions of two-pion phase space.