Resonance contributions from $\ddot{I}{‡}_{c0}$ in the charmless three-body hadronic $B$ meson decays

Abstract

Within the framework of perturbative QCD factorization, we investigate the nonfactorizable contributions to these factorization-forbidden Quasi-two-body decays $B_{(s)}\to h\ddot{I}{‡}_{c0}\to h\ddot{I}{€}^{+}\ddot{I}{€}^{-}(K^{+}{K}^{-})$ with $h=\ddot{I}€,K$. We compare our predicted branching ratios for the $B_{(s)}\to K\ddot{I}{‡}_{c0}\to K\ddot{I}{€}^{+}\ddot{I}{€}^{-}(K^{+}{K}^{-})$ decay with available experiment data as well as predictions by other theoretical studies. The branching ratios of these decays are consistent with data and other theoretical predictions. In the Cabibbo-suppressed decays $B_{(s)}\to h\ddot{I}{‡}_{c0}\to h\ddot{I}{€}^{+}\ddot{I}{€}^{-}(K^{+}{K}^{-})$ with $h={\bar{K}}^0,\ddot{I}€$, however, the values of the branching ratios are the order of $10^{-7}$ and $10^{-8}$. The ratio $R_{\ddot{I}{‡}_{c0}}$ between the decay $B^{+}\to \ddot{I}{€}^{+}\ddot{I}{‡}_{c0}\to \ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $B^{+}\to K^{+}\ddot{I}{‡}_{c0}\to K^{+}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and the distribution of branching ratios for different decay modes in invariant mass are considered in this work.

8 pages, 2 figures, accepted for publication in Chin. Phys. C