$B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach

Abstract

We investigate the $B_{d,s}^0\to f_1{f}_1$ decays in the framework of perturbative QCD(PQCD) approach with a referenced value ${\varphi }_{f_1}\sim 24^{\circ }$. Here, $f_1$ denotes the axial-vector mesons $f_1(1285)$ and $f_1(1420)$ with mixing angle ${\varphi }_{f_1}$ in the quark-flavor basis. The observables such as branching ratios, direct CP violations, and polarization fractions of the $B_s^0\to f_1{f}_1$ decays are predicted for the first time. We find that: (i) the almost pure penguin modes $B_s^0\to f_1{f}_1$ have large branching ratios in the order of $10^{-6}\sim 10^{-5}$ due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of $B_s^0\to f_n{f}_s$ and $B_s^0\to f_s{f}_s$ 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 $B_s^0\to f_1(1420)f_1(1420)$ branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the $B_{d,s}^0\to f_1{f}_1$ decay rates on ${\varphi }_{f_1}$ exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of ${\varphi }_{f_1}$ 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.

Comments: 19 pages, 3 figures, and 6 tables. the values in (A12) corrected, the numerical results and conclusions remain unchanged