How Isospin Violation Mocks ``New'' Physics: $π^0-η,η'$ Mixing in $B\to ππ$ Decays

Abstract

An isospin analysis of $B\toππ$ decays yields $\sin 2α$, where $α$ is the usual CKM angle $α\equiv arg [-V_{td}V_{tb}^\ast /(V_{ud}V_{ub}^\ast)]$, without hadronic uncertainty if isospin is a perfect symmetry. Isospin, however, is broken not only by electroweak effects but also by the u and d quark mass difference. The latter generates $π^0-η, η'$ mixing and converts the isospin-perfect triangle relation between the $B\toππ$ amplitudes to a quadrilateral. The combined isospin-violating effects impact the extracted value of $\sin 2α$ in a significant manner, particularly if the latter is small.