Study of quasi-two-body B^{0}\rightarrow T(ππ, K\bar{K},πη) decays in perturbative QCD approach

Abstract: In this study, we calculate the CP-averaged branching ratios and the direct CP-violating asymmetries of the three body decays B^{0}\rightarrow T(\pi\pi, K\bar{K},\pi\eta) in the perturbative QCD approach, where T denotes tensor mesons a_{2}(1320), K^{*}_{2}(1430), f_{2}(1270) and f^{'}_{2}(1525), and the daughter branching is f_{0}(980)\rightarrow \pi\pi, K\bar{K},f_{0}(500)\rightarrow \pi\pi, a_{0}(980)\rightarrow K\bar{K}, \pi\eta. We found the following (a) With \theta=135^{\circ}, we evaluate the branching fractions of B^{0} \rightarrow K^{*}{2}(1430)f{0}(980)[ \rightarrow \pi^ {+}\pi^{-}] to be 4.30\times10^{-6},then under the narrow-width approximation we extract the branching fraction of the decay B^{0} \rightarrow K^{*}{2}(1430)f{0}(980) to be 8.78\times10^{-6},which is consistent with the current experimental data well. (b) The decay rates for the considered decay modes are generally in the order of 10^{-8} to 10^{-5}. (c) The branching fractions are sensitive to the \theta, and the opposite is true for \phi. The \phi is really small, so the decay branching ratio has only little change, except for some decays involving f^{'}_{2}(1525). (d) The \theta and \phi can bring remarkable change to the direct CP asymmetries of pure penguin processes so that it is not 0. (e) We calculate the relative partial decay widths {\Gamma}(a_{0} \rightarrow K\overline{K})/{\Gamma}(a_{0} \rightarrow \pi\eta) and the ratio {\cal B}(f_{0} \rightarrow K^{+}K^{-})/{\cal B}(f_{0} \rightarrow \pi^{+}\pi^{-}), which are in agreement with the existing experimental values. Our results can help one to understand the internal structure of scalar mesons and the nature of tensor mesons and can be tested by future experiments.