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With the perturbative QCD approach based on factorization, we study the pure annihilation type radiative decays and $B^0\to J/\psi \gammaB^0 \to \phi\gamma(2.7^{+0.3+1.2}{-0.6-0.6})\times10^{-11}$, which is too small to be measured in the current factories of BaBar and Belle. The branching ratio of $B^0\to J/\psi \gamma({4.5^{+0.6+0.7}{-0.5-0.6}})\times10^{-7}$, which is just at the corner of being observable in the factories. A larger branching ratio is also predicted. These decay modes will help us testing the standard model and searching for new physics signals.

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