Isospin analysis of charmless B-meson decays

We discuss the determination of the CKM angle alpha using the non-leptonic two-body decays B -> pi pi, B -> rho rho and B -> rho pi using the latest data available. We illustrate the methods used in each case and extract the corresponding value of alpha. Combining all these elements, we obtain the determination alpha(dir) = (86.2(-4.0)(+4.4) boolean OR 178.4(-5.1)(+3.9))degrees. We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of the statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD dynamics involved in these decays, briefly comparing our results with theoretical expectations. For each observable of interest in the B -> pi pi, B -> rho rho and B -> rho pi systems, we perform an indirect determination based on the constraints from all the other observables available and we discuss the compatibility between indirect and direct determinations. Finally, we review the impact of future improved measurements on the determination of alpha.