The S-wave resonance contributions to the three-body decays in perturbative QCD approach

Ya Li; Ai-Jun Ma; Wen-Fei Wang; Zhen-Jun Xiao

doi:10.1140/epjc/s10052-016-4529-3

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 675
https://doi.org/10.1140/epjc/s10052-016-4529-3

Regular Article - Theoretical Physics

The S-wave resonance contributions to the three-body decays $B^0_{(s)}\rightarrow \eta _c f_0(X)\rightarrow \eta _c\pi ^+\pi ^-$ in perturbative QCD approach

Ya Li¹, Ai-Jun Ma¹, Wen-Fei Wang² and Zhen-Jun Xiao¹^*

¹ Department of Physics, Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China
² Department of Physics, Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, Shanxi, China

^* e-mail: xiaozhenjun@njnu.edu.cn

Received: 27 September 2016
Accepted: 21 November 2016
Published online: 7 December 2016

Abstract

In this paper, we study the three-body decays $B^0/B^0_s \rightarrow \eta _c f_0(X)\rightarrow \eta _c \pi ^+\pi ^-$ by employing the perturbative QCD (PQCD) factorization approach. We evaluate the S-wave resonance contributions by using the two-pion distribution amplitude $\Phi _{\pi \pi }^\mathrm{S}$ . 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 $F_{s}(\omega ^2)$ . We also use the Bugg model to parameterize the and compare the relevant theoretical predictions from different models. We found the following results: (a) the PQCD predictions for the branching ratios are $\mathcal{B}(B^0\rightarrow \eta _c f_0(500)[\pi ^+\pi ^-])= \left( 1.53 ^{+0.76}_{-0.35} \right) \times 10^{-6}$ for Breit–Wigner model and $\mathcal{B}(B^0\rightarrow \eta _c f_0(500)[\pi ^+\pi ^-])= \left( 2.31 ^{+0.96}_{-0.48} \right) \times 10^{-6}$ for Bugg model; (b) $\mathcal{B}(B_s\rightarrow \eta _c f_0(X)[\pi ^+\pi ^-] ) =\left( 5.02^{+1.49}_{-1.08} \right) \times 10^{-5}$ when the contributions from $$f_0(X)=(f_0(980),f_0(1500),f_0(1790))$$ are all taken into account; and (c) The considered decays could be measured at the ongoing LHCb experiment, consequently, the formalism of two-hadron distribution amplitudes could also be tested by such experiments.