Systematic Analysis of $B_s \to SP$ Decays in Perturbative QCD Approach

Within the perturbative QCD (PQCD) framework, we present a systematic investigation of charmless $B_s \to SP$ decays, where $S$ and $P$ denote scalar and pseudoscalar mesons, respectively. By employing two distinct structural scenarios for scalar mesons, we calculate the branching fractions and direct $CP$ asymmetries for these processes. Our results reveal branching fractions ranging from $10^{-7}$ to $10^{-5}$, values that are well within the measurable range of current experiments. A striking contrast emerges between penguin- and tree-dominated decays: while penguin-dominated processes yield larger branching fractions, tree-dominated decays exhibit significantly enhanced direct $CP$ asymmetries. In particular, the decays $B_s \to f_0(1370) \eta$ and $B_s \to a_0(1450) K$ demonstrate marked sensitivity to the choice of scalar meson scenario, offering critical constraints for identifying the optimal model once experimental data are available. Furthermore, we calculate the branching fractions of $B_s \to f_0(980)(\sigma)P$ decays in two distinct ranges of the mixing angle of $f_0(980)-\sigma$. The dependencies of both branching fractions and $CP$ asymmetries on this mixing angle are rigorously analyzed, establishing a framework essential for determining its value with future experimental results. These findings provide a robust theoretical foundation for advancing the understanding of nonleptonic $B_s$decays in QCD-based formalisms, as well as the nature of scalar mesons.