Studying the decays with mixing in the perturbative QCD approach

Qin Chang; De-Hua Yao; Xin Liu

doi:10.1140/epjc/s10052-025-13939-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 292
https://doi.org/10.1140/epjc/s10052-025-13939-y

Regular Article - Theoretical Physics

Studying the $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays with $h_{1} (1170) - h_{1} (1415)$ $h_{1}(1170){-}h_{1}(1415)$ mixing in the perturbative QCD approach

Qin Chang¹^,2, De-Hua Yao¹ and Xin Liu³^a

¹ Centre for Theoretical Physics, Henan Normal University, 453007, Xinxiang, China
² Center for High Energy Physics, Henan Academy of Sciences, 455004, Zhengzhou, China
³ Department of Physics, Jiangsu Normal University, 221116, Xuzhou, China

^a liuxin@jsnu.edu.cn

Received: 8 January 2025
Accepted: 14 February 2025
Published online: 13 March 2025

Abstract

In this paper, we study the $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays for the first time by using perturbative QCD approach up to the presently known next-to-leading order accuracy. The vertex corrections present significant contribution to the amplitude. In the calculation, the mixing between two light axial-vector mesons $h_{1} (1170)$ $h_{1}(1170)$ and $h_{1} (1415)$ $h_{1}(1415)$ are also studied in detail. The observables including the branching ratios, polarization fractions and CP asymmetries are predicted and discussed explicitly. It is found that the $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays have relatively large branching fractions, which are generally at the order of $O (10^{- 6} \sim 10^{- 3}),$ $\mathcal{O}(10^{-6}\sim 10^{-3}),$ and thus are possible to be observed by the LHCb and Belle-II experiments in the near future. Moreover, they are very sensitive to the mixing angle $θ$ $\theta$ and can be used to test the values of $θ .$ $\theta .$ In addition, some ratios between the branching fractions of $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays can provide much stronger constraints on $θ$ $\theta$ due to their relatively small theoretical errors. The $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays are generally dominated by the longitudinal polarization contributions, specifically, $f_{L} (B^{0} \to J / ψ h_{1}) > 80 %,$ $f_{L}(B^{0} \rightarrow J/\psi h_{1})>80\%,$ except for the case that $θ \sim 35^{\circ}$ $\theta \sim 35^\circ$ and $- 55^{\circ} .$ $-55^\circ .$ Unfortunately, the direct CP asymmetries of $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays are too small to be observed soon even if the effect of $θ$ $\theta$ is considered. The future precise measurements on $B^{0} \to J / ψ h_{1}$ $B^{0} \rightarrow J/\psi h_{1}$ decays are expected for testing these theoretical findings and exploring the interesting nature of $h_{1} (1170)$ $h_{1}(1170)$ and $h_{1} (1415) .$ $h_{1}(1415).$

© The Author(s) 2025

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