The $B^-\to J/ψη^\prime K^-$ reaction and the $Y(4710)$ and $K_0^*(1430)$ contributions

TL;DR

The paper investigates the decay $B^- o J/\psi\eta'^K^-$ incorporating intermediate $K_0^*(1430)$ and $Y(4710)$ resonances. It builds a formalism with hadronization into vector-vector states, loop functions, and Breit-Wigner amplitudes to model the resonant contributions, and it includes a nonresonant background in the total amplitude. Fitting to LHCb data shows that $K_0^*(1430)$ alone cannot explain the high-mass $J/\psi\eta'$ structure, but adding $Y(4710)$ yields a good description, with $M_{Y(4710)}\approx 4711$ MeV and $\Gamma_{Y(4710)}\approx 65$ MeV, in agreement with BESIII. The results favor a molecular interpretation of $K_0^*(1430)$ and suggest that measurements of $Y(4710)\to J/\psi\eta'$ could clarify the state’s nature, potentially indicating non-$c\bar{c}$ components. The study motivates further precise experimental analyses at Belle II and LHCb to confirm the $Y(4710)$ and refine its properties.

Abstract

Motivated by the recent LHCb Collaboration analysis, we have investigated the process $B^-\to J/ψη^\prime K^-$ by considering the contributions from the resonances $Y(4710)$ and $K_0^*(1430)$. Our results are in good agreement with the measured invariant mass distributions and the Dalitz plot of LHCb, which supports the existence of the $K_0^*(1430)$ and the $Y(4710)$ in the process $B^-\to J/ψη^\prime K^-$. Since the decay mode of $Y(4710)\to J/ψη'$ is Okubo-Zweig-Iizuka (OZI) suppressed for the charmonium state, the measurements of the $\mathcal{B}(Y(4710)\to J/ψη')$ through the process $B^-\to J/ψη' K^-$ or other processes is helpful to understanding the nature of the $Y(4710)$. Thus, we advocate that Belle~II and LHCb Collaborations could perform the more precise analysis to confirm the evidence of the $Y(4710)$ state, which could be helpful to reduce the experimental uncertainties of its mass and width, and to explore its nature.

Figures (6)

• Figure 1: Quark level diagram for the process $B^-\to J/\psi s(\bar{u}u+\bar{d}d+\bar{s}s)\bar{u}$.
• Figure 2: Mechanism for $K^*_0(1430)$ state.
• Figure 3: Mechanism for $Y(4710)$ state.
• Figure 4: Invariant mass distributions of $\eta^\prime K^-$ (a), $J/\psi\eta^\prime$ (b), and $J/\psi K^-$ (c) for the $B^-\to J/\psi\eta^\prime K^-$ reaction without the contribution of $Y(4710)$. The experimental data are taken from LHCb LHCb:2023qca.
• Figure 5: Invariant mass distributions of $\eta^\prime K^-$ (a), $J/\psi\eta^\prime$ (b), and $J/\psi K^-$ (c) for the $B^-\to J/\psi\eta^\prime K^-$ reaction. The experimental data are taken from LHCb LHCb:2023qca.