Isospin Amplitude Analysis of $B \to \pi\pi$ Decays within the Standard Model

Taking into account the recent measurements of the branching ratios and CP asymmetries in the $B \to \pi\pi$ decays by the BABAR and BELLE collaborations, an amplitude analysis based on the isospin symmetry is reported. These data allow to get an independent determination of the CKM unitarity-triangle angle $\gamma$. One of the best-fit solutions gives the range $\gamma = (65 \pm 5)^\circ$, in excellent agreement with the global CKM fit within the Standard Model. The other parameters from this fit confirm the earlier analyses that the data on $B \to \pi\pi$ decays require various topological amplitudes (neglecting the electroweak ones) to be of comparable magnitude with large strong-phase differences.