$f_J(2220)$ and Hadronic $\bar B^0_s$ Decays

Abstract

We study the hadronic $\bar B^0_s$ decays based on the existence of the resonant state $f_J(2220)$. In particular, we are able to explain the unexpected large experimental result of ${\cal B}(\bar B^0_s\to J/\psi p\bar p) =(3.0^{+1.2}_{-1.1}\pm 0.52\pm 0.03)\times 10^{-6}$ measured recently by the LHCb collaboration due to the resonant contribution in $\bar B^0_s\to J/\psi f_J(2220)$ with $f_J(2220) \to p\bar p$, while it is estimated to be at most of order $10^{-9}$ in terms of the OZI rule without the resonance. In addition, we find that ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to) p\bar p)=(4.05\pm 2.46)\times 10^{-7}$, ${\cal B}(\bar B^0_s\to J/\psi(f_J\to)\pi\pi)=(15.6\pm 15.2)\times 10^{-6}$ and ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to)\pi\pi)=(21.2\pm 20.9)\times 10^{-7}$, while ${\cal B}(\bar B^0_s\to J/\psi(f_J\to)K\bar K)<1.6\times 10^{-5}$ and ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to)K\bar K)<2.2\times 10^{-6}$. Moreover, we predict that the decay branching ratios of $\bar B^0_s\to (J/\psi\,,D^{*0})\Lambda\bar \Lambda$ are $(2.68\pm1.23)\times 10^{-7}$ and $(2.25\pm0.80)\times 10^{-6}$. Some of the predicted $\bar B^0_s$ decays are accessible to the experiments at the LHCb.