$B\to K\bar{K}(\pi \eta )h$ decays in the presence of isovector scalar resonances $a_0(980,1450)$

Abstract

Different from the previous treatment in a two-body framework, we introduce the dimeson distribution amplitudes (DAs) to describe the strong dynamics between the S-wave resonances $a_0(980,1450)$ and the $K\bar{K}(\pi \eta )$ pair, where the Gegenbauer coefficient required is determined from the experimental data on the time-like form factors involved. The branching ratios and direct CP asymmetries of the decays $B\to a_0^{(\prime )}h\to K\bar{K}(\pi \eta )h$, with $a_0=a_0(980)$, $a_0^{\prime }=a_0(1450)$ and $h$ referring to a pion or a kaon, are then calculated in the perturbative QCD (PQCD) approach. We find that the branching ratios of the corresponding quasi-two-body decays $B\to a_0^{(\prime )}K$ obtained with the narrow width approximation are closer to those predicted in the QCD factorization (QCDF) approach compared to the previous PQCD calculations, no matter a three-body or a two-body framework is assumed. Furthermore, all our predictions for these $B\to a_0^{(\prime )}K$ decays are below the current experimental upper limits except for those of decays $B^0\to a_0^{(\prime )-}{K}^{+}$, which are (slightly) larger than the upper limits. Under the narrow width approximation, the branching ratios of the decays $B^{+}\to a_0^{(\prime )+}{\pi }^0$, $B^0\to a_0^{(\prime )+}{\pi }^{-}$ and $B^0\to a_0^{(\prime )0}{\pi }^0$ are comparable to or agree well with the previous PQCD and the QCDF calculations. While for the decays $B^{+}\to a_0^{(\prime )0}{\pi }^{+}$ and $B^0\to a_0^{(\prime )-}{\pi }^{+}$, their branching ratios are predicted to be unexpectedly large, for example, the obtained branching ratio of decay $B^{+}\to a_0^0{\pi }^{+}$ is even higher than the current experimental upper limit.

Comments: 22 pages, 2 figures