Pure annihilation decays of Bs0 → a0+ a0− and Bd0 → ${K}_{0}^{* +}$ ${K}_{0}^{* -}$ in the PQCD approach

Yutong Chen(陈禹同),Zewen Jiang(蒋泽文),Xin Liu(刘新)

Table 3. The tree and penguin decay amplitudes(in units of 10−3 GeV3) in S1 of the pure annihilation ${B}_{d}^{0}\to {K}_{0}^{* +}{K}_{0}^{* -}$ and ${B}_{s}^{0}\to {a}_{0}^{+}{a}_{0}^{-}$ decays in the PQCD approach, where the results in the parentheses are the corresponding amplitudes of the ${\bar{B}}_{d}^{0}\to {K}_{0}^{* +}{K}_{0}^{* -}$ and ${\bar{B}}_{s}^{0}\to {a}_{0}^{+}{a}_{0}^{-}$ decays, and only the central values are considered for clarifications.

Modes Tree diagrams(T3A) Penguin diagrams(T3A) ${B}_{d}^{0}\to {K}_{0}^{* }{\left(800\right)}^{+}{K}_{0}^{* }{(800)}^{-}$ $\begin{array}{c}0.551-{\rm{i}}\ 1.920\ \\ (-1.615+{\rm{i}}\ 1.176)\end{array}$ $\begin{array}{c}-1.160-{\rm{i}}\ 0.054\ \\ (-0.779-{\rm{i}}\ 0.861)\end{array}$ ${B}_{d}^{0}\to {K}_{0}^{* }{\left(1430\right)}^{+}{K}_{0}^{* }{(1430)}^{-}$ $\begin{array}{c}1.633-{\rm{i}}\ 1.433\ \\ (-2.169+{\rm{i}}\ 0.126)\end{array}$ $\begin{array}{c}0.245-{\rm{i}}\ 1.222\ \\ (1.040-{\rm{i}}\ 0.687)\end{array}$ ${B}_{s}^{0}\to {a}_{0}{\left(980\right)}^{+}{a}_{0}{\left(980\right)}^{-}$ $\begin{array}{c}-0.013-{\rm{i}}\ 0.504\ \\ (-0.300+{\rm{i}}\ 0.406)\end{array}$ $\begin{array}{c}6.906+{\rm{i}}\ 1.827\ \\ (6.906+{\rm{i}}\ 1.827)\end{array}$ ${B}_{s}^{0}\to {a}_{0}{\left(1450\right)}^{+}{a}_{0}{\left(1450\right)}^{-}$ $\begin{array}{c}0.738-{\rm{i}}\ 0.619\ \\ (-0.963+{\rm{i}}\ 0.035)\end{array}$ $\begin{array}{c}-2.332+{\rm{i}}\ 10.678\ \\ (-2.332+{\rm{i}}\ 10.678)\end{array}$