Enhanced Quark-Loop Contribution to Pure Annihilation Nonleptonic B-meson decays in PQCD approach

In this study, we conduct an enhanced investigation of pure annihilation-type charmless hadronic B-decays within the framework of the PQCD approach. Specifically, we account for the quark-loop enhanced contribution to various decay processes at the next-to-leading order(NLO) in the strong coupling constant $\alpha_s$. The NLO amplitudes possess large imaginary parts that have signs opposite to those of the leading-order amplitudes. This cancellation effect implies that the NLO contribution does not significantly influence the branching ratios of the processes under consideration. However, the NLO effect explored in this work constitutes an important source of the strong phases in the weak - annihilation non-leptonic $\bar B_q$-meson decay amplitudes. As a result, it can have a substantial impact on CP - violating observables such as the direct CP asymmetry ${\cal A}_{\rm CP}^{\rm dir}$ and mixing induced CP asymmetry ${\cal A}_{\rm CP}^{\rm mix}$. The numerical result evidently revealed that NLO QCD correction significantly enhances both ${\cal A}_{\rm CP}^{\rm dir}$ and ${\cal A}_{\rm CP}^{\rm mix}$ of the pure annihilation type B decay processes.