Study of the quasi-two-body decays B^{0}_{s} rightarrow psi (3770) (psi (3686))pi ^+pi ^- with perturbative QCD approach

Ze-Rui Liang,Feng-Bo Duan,Xian-Qiao Yu

doi:10.1140/epjc/s10052-019-6877-2

Ze-Rui Liang, Feng-Bo Duan + Show 1 more

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https://doi.org/10.1140/epjc/s10052-019-6877-2

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Abstract

In this note, we study the contributions from the S-wave resonances, f_{0}(980) and f_{0}(1500), to the B^{0}_{s}rightarrow psi (3770)pi ^ {+}pi ^{-} decay by introducing the S-wave pi pi distribution amplitudes within the framework of perturbative QCD approach. Both the resonant and the non-resonant contributions are contained in the scalar form factor in the S-wave distribution amplitude Phi ^S_{pi pi }. Since the vector charmonium meson psi (3770) is a S–D wave mixed state, we calculate the branching ratios of S-wave and D-wave, respectively, and the results indicate that f_{0}(980) is the main contribution of the considered decay, and the branching ratio of the psi (2S) mode is in good agreement with the experimental data. We also take the S–D mixed effect into the B^{0}_{s}rightarrow psi (3686)pi ^ {+}pi ^{-} decay. Our calculations show that the branching ratio of B^{0}_{s}rightarrow psi (3770)(psi (3686))pi ^ {+}pi ^{-} can be at the order of 10^{-5}, which can be tested by the running LHCb experiments.

Highlights

The Heavy Flavor Averaging Group [6] have collected lots of world averages of measurements of B-hadron properties from LHCb [7,8,9,10,11,12,13,14], Belle [15] and BaBar [16,17,18] and other collaborations, in which the LHCb Collaboration have measured sizable direct CP asymmetries in kinematic regions
Since the vector charmonium meson ψ(3770) is a S–D wave mixed state, we calculate the branching ratios of S-wave and D-wave, respectively, and the results indicate that f0(980) is the main contribution of the considered decay, and the branching ratio of the ψ(2S) mode is in good agreement with the experimental data
In the perturbative QCD (pQCD) approach which is based on the kT factorization theorem, the three-body decay can be simplified into a two-body case by bringing in two-hadron distribution amplitudes [43,44], which contain the information of both resonance and non-resonance

Summary

Introduction

The Heavy Flavor Averaging Group [6] have collected lots of world averages of measurements of B-hadron properties from LHCb [7,8,9,10,11,12,13,14], Belle [15] and BaBar [16,17,18] and other collaborations, in which the LHCb Collaboration have measured sizable direct CP asymmetries in kinematic regions. The contribution studies within non-resonance have been performed by using a heavy meson chiral perturbative theory approach in Refs. J. C (2019) 79:370 from experiment or calculated by several nonperturbative approaches, and can be regarded as nonperturbative input, are the distribution amplitude of the B meson, the h1h2 pair and h3, respectively. [46], the authors make tentative calculations for different mixing solutions of the B meson exclusive decay B → ψ(3770)K with the QCD factorization, and they drew the conclusion that when taking account of higher-twist effects and adopting the S–D mixing angle θ = −(12 ± 2)◦ (which the widely accepted value), the branching ratio of the decay B → ψ(3770)K can fit the experimental data well. We will finish this paper with a brief summary

The theoretical framework and the wave function

The decay amplitudes

Nc αs 9π

Numerical results and discussions

Summary