Phys. Rev. D 91, 094024 (2015) - $S$-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

$S$ -wave resonance contributions to the $B_{(s)}^{0} \to J / ψ π^{+} π^{-}$ and $B_{s} \to π^{+} π^{-} μ^{+} μ^{-}$ decays

Wen-Fei Wang, Hsiang-nan Li, Wei Wang, and Cai-Dian Lü

Phys. Rev. D 91, 094024 – Published 21 May 2015

Abstract

We study $S$ -wave resonance contributions to the $B_{(s)}^{0} \to J / ψ π^{+} π^{-}$ and $B_{s} \to π^{+} π^{-} μ^{+} μ^{-}$ 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 Flatté 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 $C P$ asymmetries of other three-body hadronic $B$ meson decays in various localized regions of two-pion phase space.

Received 3 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.094024

Authors & Affiliations

Wen-Fei Wang^1,*, Hsiang-nan Li^2,†, Wei Wang^3,4,‡, and Cai-Dian Lü^1,4,§

¹Center for Future High Energy Physics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
²Institute of Physics, Academia Sinica, Taipei, Taiwan 115, Republic of China
³INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁴State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

^*wangwf@ihep.ac.cn
^†hnli@phys.sinica.edu.tw
^‡wei.wang@sjtu.edu.cn
^§lucd@ihep.ac.cn

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Vol. 91, Iss. 9 — 1 May 2015

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Physical Review D

covering particles, fields, gravitation, and cosmology

$S$ -wave resonance contributions to the $B_{(s)}^{0} \to J / ψ π^{+} π^{-}$ and $B_{s} \to π^{+} π^{-} μ^{+} μ^{-}$ decays

Wen-Fei Wang, Hsiang-nan Li, Wei Wang, and Cai-Dian Lü

Phys. Rev. D 91, 094024 – Published 21 May 2015

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Physical Review D

covering particles, fields, gravitation, and cosmology

S-wave resonance contributions to the B(s)0→J/ψπ+π− and Bs→π+π−μ+μ− decays

Wen-Fei Wang, Hsiang-nan Li, Wei Wang, and Cai-Dian Lü

Phys. Rev. D 91, 094024 – Published 21 May 2015

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$S$ -wave resonance contributions to the $B_{(s)}^{0} \to J / ψ π^{+} π^{-}$ and $B_{s} \to π^{+} π^{-} μ^{+} μ^{-}$ decays