Direct CP Violation and Isospin Triangles of B->\pi\pi Decays

The recent observation of B^0_d->\pi^0\pi^0 and \bar{B}^0_d->\pi^0\pi^0 decay modes allows us to make a fresh isospin analysis of B->\pi\pi transitions. We find that current experimental data can impose some model-independent constraints on the parameter space of direct CP violation in B_d->\pi^+\pi^- and B_d->\pi^0\pi^0. Furthermore, we establish a direct relationship between the weak phase \alpha and the charge-averaged branching fractions and CP-violating asymmetries of B->\pi\pi decays.