Isospin-breaking effects on alpha extracted in B --> pi pi, rho rho, rho pi

Abstract

Isospin-breaking in B --> pi pi caused by pi^0-eta-eta' mixing is studied in a model-independent way using flavor SU(3). Measured branching ratios for B^+ --> pi^+ pi^0, B^+ --> pi^+ eta^(') and B^0 --> pi^0 eta^(') imply an uncertainty in alpha smaller than 1.4 degree. We find a negligible effect of pi^0-eta-eta' mixing on alpha in B --> rho pi. Characterizing the effect of rho^0-omega mixing in B --> rho rho and in B --> rho pi by the two-pion invariant mass dependence, we point out a way of constraining this effect experimentally or eliminating it altogether. We show that a model-independent shift in alpha caused by electroweak penguin amplitudes in B --> pi pi and B --> rho rho, \Delta alpha_{EWP}=1.5+- 0.3 degree, may be slightly different in B --> rho pi. Other sources of isospin-breaking in these processes are briefly discussed.