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Home > Nuclear Physics B (Elsevier) > The three-body decays B ( s ) → ρf 0 ( X )→ ρπ − π + in pQCD factorization approach |

Wang, Hui-sheng (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China) ; Wang, Xing-lin (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China) ; Zheng, Fa-nong (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China) ; Liu, Shao-min (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China) ; Cao, Jing (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China) ; Wang, Qing-song (School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, People's Republic of China)

18 March 2017

**Abstract: **In this paper, we study three-body decays B(s)→ρf0(X)→ρπ−π+ in the perturbative QCD (pQCD) factorization approach. By using two-pion distribution amplitudes (DAs), these decays can proceed mainly via quasi-two-body channels. The Flatté model for the f0(980) resonance and the Breit–Wigner formula for the f0(500) , f0(1500) , and f0(1790) resonances are adopted to parameterize the time-like scalar form factors. We also use Bugg's model for the wide f0(500) as a comparison. We evaluate S-wave resonance contributions, and show the contributions to the B(s)→ρπ+π− decay spectrums with respect to the two-pion invariant mass M(π+π−) . The pQCD prediction of B→ρf0(500) is B(B0→ρ0f0(500))=4.43×10−8 , B(B+→ρ+f0(500))=3.84×10−8 for Breit–Wigner model, and B(B0→ρ0f0(500))=4.91×10−8 , B(B+→ρ+f0(500))=4.07×10−8 for Bugg's model. We also predict other resonance contributions B(Bs→ρ0f0(980))=8.91×10−8 , B(Bs→ρ0f0(1500))=1.43×10−8 and B(Bs→ρ0f0(1790))=2.78×10−9 . This study in pQCD approach can provide a ready reference to the running and forthcoming experiments. Further improvements in theories and experiments are expected so that we can understand the inner structure of the scalar mesons f0 .

**Published in: ****Nuclear Physics B (2017)**
**Published by: **Elsevier

**DOI: **10.1016/j.nuclphysb.2017.03.008

**License: **CC-BY-3.0