Direct CP Violation and Isospin Triangles of B->ππDecays

Abstract

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