Search

The axial-vector mesons $f_1(1285)$ and $f_1(1420)$ are particularly viewed as the mixtures of flavor states $f_n$ and $f_s$ with mixing angle $\varphi$. In order to determine this angle, we study the $B_{d,s}^0\to J/\psi f_1(1285,1420)$ and $B_{d,s}^0\to \eta_c f_1(1285,1420)$ decays in perturbative QCD (PQCD) approach, including the effects of vertex corrections, nonfactorizable diagrams and penguin operators. Not only the branching fractions, but also the direct $CP$ asymmetries and the polarization fractions are calculated. It is found that the branching fractions of these decays are large enough to be measured in the running LHCb and Belle-II experiments. Moreover, in comparison with the observed ${\cal B}(B_{d,s}^0 \to J/\psi f_1(1285))$, $B_s^0 \to (J/\psi, \eta_c) f_1(1420)$ decays have large branching fractions, which could be measured promisingly through $f_1(1420) \to K_S^0 K^\pm \pi^\mp$ in experiments. We also propose several ratios that could be used to further constrain the absolute value of the mixing angle $\varphi$, but its sign cannot be determined yet in these decays. The direct CP asymmetries of these decays indicate the penguin pollution in the $B_d^0 \to (J/\psi, \eta_c) f_1$ decays cannot be neglected. We acknowledge that there are large theoretical uncertainties arising from the distribution amplitudes of axial-vector mesons and charmonium states, and more precise nonperturbative parameters are called. The comparisons between our results and future experimental data would help us to understand the nature of $f_1$ states and to test the PQCD approach., Comment: 18 pages, 3 figures, journal version, published in EPJC

We investigate the ${B}_{d,s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decays in the framework of perturbative QCD (PQCD) approach with a referenced value ${\ensuremath{\phi}}_{{f}_{1}}\ensuremath{\sim}24\ifmmode^\circ\else\textdegree\fi{}$. Here, ${f}_{1}$ denotes the axial-vector mesons ${f}_{1}(1285)$ and ${f}_{1}(1420)$ with mixing angle ${\ensuremath{\phi}}_{{f}_{1}}$ in the quark-flavor basis. The observables such as branching ratios, direct $CP$ violations, and polarization fractions of the ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decays are predicted for the first time. We find that (i) the almost pure penguin modes ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ have large branching ratios in the order of ${10}^{\ensuremath{-}6}\ensuremath{\sim}{10}^{\ensuremath{-}5}$ due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{n}{f}_{s}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{s}{f}_{s}$ with ${f}_{n}$ and ${f}_{s}$ being the quark-flavor states of ${f}_{1}$ mesons. (ii) The observables receive important contributions from the weak annihilation diagrams in the PQCD approach. In particular, without the annihilation contributions, the ${B}_{s}^{0}\ensuremath{\rightarrow}{f}_{1}(1420){f}_{1}(1420)$ branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the ${B}_{d,s}^{0}\ensuremath{\rightarrow}{f}_{1}{f}_{1}$ decay rates on ${\ensuremath{\phi}}_{{f}_{1}}$ exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of ${\ensuremath{\phi}}_{{f}_{1}}$ inversely. All the PQCD predictions await for the (near) future examinations at Large Hadron Collider beauty and/or Belle-II experiments to further understand the properties of the axial-vector mesons and the perturbative dynamics released from the considered decay modes.