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

Abstract

We study $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ 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 Flatté 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.

Comments: 13 pages, 3 figures