We calculate the branching ratio of B→J/ψπ0 with a mixed formalism that combines the QCD-improved factorization and the perturbative QCD approaches. The result is consistent with experimental data.The quite small penguin contribution in B→J/ψπ0 decay can be calculated with this method. We suggest two methods to extract the weak phase β. One is through the dependence of the mixing induced CP asymmetry SJ/ψπ0 on the weak phase β, the other is from the relation of the total asymmetry ACP with the weak phase β. Our results show that the deviation △SJ/ψπ0 of the mixing induced CP asymmetry from sin(-2β) is of O(10-3) and has much less uncertainty. The above O(10-3) deviation can provide a good reference for identifying new physics.
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