Towards a precision determination ofαinB→ππdecays

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 ${\sigma }_{\alpha }^{\mathrm{IB}}$ 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 ${\sigma }_{\alpha }^{\mathrm{IB}}$ can potentially be controlled to $\mathcal{O}(1°)$.