Study of decaying into and , , or with final state interactions

Hiwa A. Ahmed; C. W. Xiao

doi:10.1140/epja/s10050-023-01146-w

2024 Impact factor 2.8

Hadrons and Nuclei

Eur. Phys. J. A (2023) 59: 245
https://doi.org/10.1140/epja/s10050-023-01146-w

Regular Article –Theoretical Physics

Study of ${\bar{B}}_{(s)}^{0}$ $\bar{B}^0_{(s)}$ decaying into $D^{0}$ and $π^{+} π^{-}$ $\pi ^{+}\pi ^{-}$ , $K^{+} K^{-}$ $K^{+}K^{-}$ , or $π^{0} η$ $\pi ^{0}\eta$ with final state interactions

Hiwa A. Ahmed¹^,2 and C. W. Xiao³^,4^b

¹ Department of Physics, College of Science, Charmo University, Chamchamal, 46023, Sulaymaniyah, Iraq
² School of Nuclear Science and Technology, University of Chinese Academy of Sciences, 100049, Beijing, China
³ Department of Physics, Guangxi Normal University, 541004, Guilin, China
⁴ School of Physics, Central South University, 410083, Changsha, China

^b xiaochw@gxnu.edu.cn

Received: 20 October 2022
Accepted: 4 October 2023
Published online: 27 October 2023

Abstract

The resonant contributions in the decays ${\bar{B}}_{(s)}^{0} \to D^{0} π^{+} π^{-}$ $\bar{B}^0_{(s)} \rightarrow D^0 \pi ^{+}\pi ^{-}$ , ${\bar{B}}_{(s)}^{0} \to D^{0} K^{+} K^{-}$ $\bar{B}^0_{(s)} \rightarrow D^0 K^{+}K^{-}$ , and ${\bar{B}}^{0} \to D^{0} π^{0} η$ $\bar{B}^{0} \rightarrow D^{0} \pi ^{0}\eta$ are investigated by considering the final state interactions within the chiral unitary approach, where the scalar resonances $f_{0} (500)$ $f_{0}(500)$ , $f_{0} (980)$ $f_{0}(980)$ , and $a_{0} (980)$ $a_{0}(980)$ are dynamically generated from the final state interactions. In addition, the vector mesons $ρ$ $\rho$ , $ϕ$ $\phi$ and $D_{0}^{*} (2300)$ $$D^*_0(2300)$$ directly produced in p wave are also taken into account. From the invariant mass distributions of $B^{0}$ $B^{0}$ decays, it is found that the contributions of $f_{0} (500)$ $f_{0}(500)$ and $a_{0} (980)$ $a_{0}(980)$ are remarkably larger than those of $f_{0} (980)$ $f_{0}(980)$ . However, for the case of $B_{s}^{0}$ $B^{0}_{s}$ decays only a clear structure close to the $K^{+} K^{-}$ $K^{+} K^{-}$ threshold appears, which corresponds to the $f_{0} (980)$ $f_{0}(980)$ state and has no signal for the $f_{0} (500)$ $f_{0}(500)$ resonance. For the decay ${\bar{B}}_{s}^{0} \to D^{0} K^{+} K^{-}$ $\bar{B}^0_s \rightarrow D^0 K^{+}K^{-}$ , the $K^{+} K^{-}$ $K^{+} K^{-}$ invariant mass distributions are consistent with the experimental data up to 1.1 GeV, and the dominant contributions come from the vector meson $ϕ$ $\phi$ . Moreover, the branching fractions and the ratios of branching fractions are also studied, some of which are compatible with the experimental measurements. The branching fraction $Br ({\bar{B}}^{0} \to D^{0} a_{0} (980) [a_{0} (980) \to π^{0} η]) = (6.08 \pm 0.72) \times 10^{- 5}$ $\text {Br}(\bar{B}^{0} \rightarrow D^{0} a_{0}(980) [a_{0}(980) \rightarrow \pi ^{0}\eta ])=(6.08 \pm 0.72)\times 10^{-5}$ and the ratio of branching fractions $Br ({\bar{B}}^{0} \to D^{0} f_{0} (980)) / Br ({\bar{B}}^{0} \to D^{0} a_{0} (980)) = 0.13 \pm 0.03$ $\text {Br}(\bar{B}^{0}\rightarrow D^0 f_{0}(980))/\text {Br}(\bar{B}^{0}\rightarrow D^0 a_{0}(980))=0.13 \pm 0.03$ are predicted.

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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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Study of ${\bar{B}}_{(s)}^{0}$ $\bar{B}^0_{(s)}$ decaying into $D^{0}$ and $π^{+} π^{-}$ $\pi ^{+}\pi ^{-}$ , $K^{+} K^{-}$ $K^{+}K^{-}$ , or $π^{0} η$ $\pi ^{0}\eta$ with final state interactions