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We study charmless pure annihilation type radiative B decays within the QCDfactorization approach. After adding the vertex corrections to the naivefactorization approach, we find that the branching ratios of$\bar{B}^0_d\to\phi\gamma$, $\bar{B}^0_s\to\rho^0\gamma$ and$\bar{B}^0_s\to\omega\gamma$ within the standard model are at the order of$\mathcal{O}(10^{-12})$, $\mathcal{O}(10^{-10})$ and $\mathcal{O}(10^{-11})$,respectively. The smallness of these decays in the standard model makes themsensitive probes of flavor physics beyond the standard model. To explore theirphysics potential, we have estimated the contribution of $Z^\prime$ boson inthe decays. Within the allowed parameter space, the branching ratios of thesedecay modes can be enhanced remarkably in the non-universal $Z^\prime$ model:The branching ratios can reach to $\mathcal{O}(10^{-8})$ for $\bar B_s^0 \to\rho^0(\omega)\gamma$ and $\mathcal{O}(10^{-10})$ for the $\bar B_d^0 \to \phi\gamma$, which are large enough for LHC-b and/or Super B-factories to detectthose channels in near future. Moreover, we also predict large CP asymmetriesin suitable parameter space. The observation of these modes could in turn helpus to constrain the $Z'$ mass within the model.

Annihilation-Type Charmless Radiative Decays of B Meson in Non-universal Z^\prime Model