Towards a Precision Determination of alpha in B \to pi pi Decays

An assumption of isospin symmetry permits the determination of sin(2 alpha) from the experimental study of B\to pi pi decays. Isospin, however, is merely an approximate symmetry; its breaking predicates a theoretical systematical error sigma_\alpha^{\rm IB} in the extraction of alpha. We focus on the impact of \pi^0-\eta,\eta^\prime mixing, as well as the manner in which it is amenable to empirical constraint, and determine that \sigma_\alpha^{\rm IB} can potentially be controlled to {\cal O}(1^\circ).