How isospin violation mocks "new" physics: π⁰-η,η′ mixing in B→ππ decays

An isospin analysis of B→ππ decays yields sin 2α, where α≡arg[-V_tdV_tb*/(V_udV _ub*)] and V_ij is a CKM matrix element, 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 drives π⁰-η,η′ mixing and converts the isospin-perfect triangle relation between the B→ππ 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.