B→K1π(K)decays in the perturbative QCD approach

Abstract

Within the framework of the perturbative QCD approach, we study the two-body charmless decays $B\ensuremath{\rightarrow}{K}_{1}(1270)({K}_{1}(1400))\ensuremath{\pi}(K)$. We find the following results: (i) The decays ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}_{1}(1270{)}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}_{1}(1400{)}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ are incompatible with the present experimental data. There exists a similar situation for the decays ${\overline{B}}^{0}\ensuremath{\rightarrow}{a}_{1}(1260{)}^{+}{K}^{\ensuremath{-}}$, ${b}_{1}(1235{)}^{+}{K}^{\ensuremath{-}}$, which are usually considered that the nonperturbative contributions are needed to explain the data. But the difference is that the nonperturbative contributions seem to play opposite roles in these two groups of decays. (ii) The pure annihilation type decays ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}_{1}^{\ifmmode\pm\else\textpm\fi{}}(1270){K}^{\ensuremath{\mp}}$, ${K}_{1}^{\ifmmode\pm\else\textpm\fi{}}(1400){K}^{\ensuremath{\mp}}$ are good channels to test whether an approach can be used to calculate correctly the strength of the penguin-annihilation amplitudes. Their branching ratios are predicted at $1{0}^{\ensuremath{-}7}$ order, which are larger than the QCDF results. (iii) The dependence of the direct $CP$-violating asymmetries of these decays on the mixing angle ${\ensuremath{\theta}}_{{K}_{1}}$ are also considered.