Axial-vector $f_1(1285)-f_1(1420)$ mixing and $B_s o J/\psi (f_1(1285), f_1(1420))$ decays

摘要

Inspired by the very recent LHCb measurements of $B_s \to J/\psi f_1(1285)$and the good agreement between the perturbative QCD predictions and the datafor many $B \to J/\psi V$ decays, we here investigate the $B_s \to J/\psif_1(1285)$ and $B_s \to J/\psi f_1(1420)$ decays for the first time byemploying the perturbative QCD (pQCD) approach, in which the $1^3P_1$ states$f_1(1285)$ and $f_1(1420)$ are believed to be the mixture of flavor singlet$f_1$ and octet $f_8$ or of quark-flavor states $f_{1q}$ and $f_{1s}$. We showthat the pQCD predictions for the branching ratio of $B_s \to J/\psi f_1(1285)$agree well with the data within errors for the mixing angle $\theta_{^3P_1}\approx 20^\circ (\phi_{^3P_1} \approx 15^\circ)$ between $f_1 (f_{1q})$ and$f_8 (f_{1s})$ states. Furthermore, the branching ratio of $B_s \to J/\psif_1(1420)$ and the large transverse polarization fractions in these twoconsidered channels are also predicted and will be tested by the LHC and theforthcoming Super-B factory experiments. Based on the decay rates of $B_s \toJ/\psi f_1(1285)$ and $B_s \to J/\psi f_1(1420)$ decay modes predicted in thepQCD approach, the extracted mixing angle between $f_1(1285)$ and $f_1(1420)$is basically consistent with currently available experimental measurements andlattice QCD analysis within still large theoretical errors.