S-wave resonance contributions to theB(s)0→J/ψπ+π−andBs→π+π−μ+μ−decays

Abstract

We study $S$-wave resonance contributions to the ${B}_{(s)}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decays in the perturbative QCD 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 parametrize the timelike 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.