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

Abstract

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 data for many $B\to J/\psi V$ decays, we here investigate the $B_s\to J/\psi f_1(1285)$ and $B_s\to J/\psi f_1(1420)$ decays for the first time by employing the perturbative QCD (pQCD) approach, in which the $1^3{P}_1$ 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 show that 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 ${\theta }_{{}^3{P}_1}\approx 20^{\circ }({\varphi }_{{}^3{P}_1}\approx 15^{\circ })$ between $f_1(f_{1q})$ and $f_8(f_{1s})$ states. Furthermore, the branching ratio of $B_s\to J/\psi f_1(1420)$ and the large transverse polarization fractions in these two considered channels are also predicted and will be tested by the LHC and the forthcoming Super-B factory experiments. Based on the decay rates of $B_s\to J/\psi f_1(1285)$ and $B_s\to J/\psi f_1(1420)$ decay modes predicted in the pQCD approach, the extracted mixing angle between $f_1(1285)$ and $f_1(1420)$ is basically consistent with currently available experimental measurements and lattice QCD analysis within still large theoretical errors.

Comments: 10 pages, 1 figure, 1 table; Contents improved and references added; Accepted for publication as a Brief Report in Physical Review D