Study of the nonleptonic charmless $B$ ${\to}$ $SS$ decays with the QCD factorization approach

Inspired by the brilliant prospects of the ongoing $B$ meson experiments, the hadronic charmless $B$ ${\to}$ $SS$ decays are studied by considering the next-to-leading (NLO) contributions with the QCD factorization approach, where $S$ denotes the scalar mesons $K_{0}^{\ast}(1430)$ and $a_{0}(1450)$. Branching ratios and $CP$ violating asymmetries are estimated with the updated values of hadronic parameters obtained from a covariant light-front quark model, for two scenarios where the scalar mesons are the $1^{3}P_{0}$ and $2^{3}P_{0}$ states. It is found that the NLO contributions are very important for the $B$ ${\to}$ $SS$ decays; For the $B$ ${\to}$ $a_{0}(1450)K_{0}^{\ast}(1430)$ and $B_{s}$ ${\to}$ $K_{0}^{\ast}(1430)\overline{K}_{0}^{\ast}(1430)$ decays, branching ratios can reach up to the order of ${\cal O}(10^{-5})$ by assuming that the scalar mesons are the $1P$ states, and should first be investigated in the future experiments.