Analysis of $B \to a_1(1260)(b_1(1235))K^*$ decays in the perturbative QCD approach

Abstract

Within the framework of perturbative QCD approach, we study the charmless two-body decays $B\to a_1(1260)K^*, b_1(1235)K^*$. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Our predictions for the branching ratios are consistent well with the QCDF results within errors, but much larger than the naive factorization approach calculation values. (b) We predict that the anomalous polarizations occurring in the decays $B\to ϕK^*, ρK^*$ also happen in the decays $B\to a_1K^*$, while do not happen in the decays $B\to b_1K^*$. Here the contributions from the annihilation diagrams play an important role to explain the lager transverse polarizations in the decays $B\to a_1K^*$, while they are not sensitive to the polarizations in decays $B\to b_1K^*$. (c) Our predictions for the direct CP-asymmetries agree well with the QCDF results within errors. The decays $\bar B^0\to b^{+}_1K^{*-}, B^-\to b^{0}_1K^{*-}$ have larger direct CP-asymmetries, which could be measured by the present LHCb experiments.