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Probing new physics in $B\to J/Ψπ^0$ decay

We calculate the branching ratio of $B\to J/Ψπ^{0}$ 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 $B\to J/Ψπ^{0}$ 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 $S_{J/Ψπ^{0}}$ on the weak phase$β$, the other is from the relation of the total asymmetry $A_{CP}$ with the weak phase $β$. Our result shows that the deviation $ \bigtriangleup S_{J/ψπ^0}$ of the mixing induced CP asymmetry from $Sin(-2β)$ is of $ \mathcal{O}(10^{-3})$ and has much less uncertainty. The above $ \mathcal{O}(10^{-3})$ deviation can provide a good reference for identifying new physics.