Analysis of the Decays B-> ππand πK with QCD Factorization in the Heavy Quark Limit

In this work, we calculate the branching ratios and CP asymmetries of the decays of $B \to \pi \pi$ and $\pi K$ in the frame of QCD factorization in the heavy quark limit. We also compare the results with the estimates by using conventional factorization and experimental measurements.