Phenomenological studies on the $B_{d,s}^0\to J/\psi f_0(500)[f_0(980)]$ decays

Abstract

Encouraged by the global agreement between theoretical predictions and experimental measurements for $B\to J/\psi V$ decays, we extend that perturbative QCD formalism to $B_{d,s}^0\to J/\psi f_0(500)[f_0(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of $f_0(500)$ and $f_0(980)$. With the angle ${\varphi }_f\approx 25^{\circ }$ of the $f_0(500)-f_0(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the $B_d^0\to J/\psi f_0(500)(\to {\pi }^{+}{\pi }^{-})$ and $B_{d,s}^0\to J/\psi f_0(980)(\to {\pi }^{+}{\pi }^{-})$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging $B_s^0\to J/\psi f_0(500)(\to {\pi }^{+}{\pi }^{-})$ one. Then, we further explore the relevant observables of the $B_{d,s}^0\to J/\psi f_0(500)[f_0(980)]$ decays, which could provide further constraints on the mixing angle ${\varphi }_f$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict $\mathrm{BR}(B_d^0\to J/\psi f_0(980)(\to K^{+}{K}^{-}))=5.8_{-2.9}^{+3.1}\times 10^{-7}$ and $\mathrm{BR}(B_s^0\to J/\psi f_0(980)(\to K^{+}{K}^{-}))=4.6_{-2.3}^{+2.6}\times 10^{-5}$. All theoretical predictions await the future examinations with high precision.

Comments: RevTex file, 15 pages, 5 figures; final version to appear in PRD