Towards More Precise Determinations of the Quark Mixing Phase β.

We derive a new flavor symmetry relation for the determination of the weak phase β=ϕ_{1} from time-dependent CP asymmetries and B→J/ψP decay rates. In this relation, the contributions to sin2β proportional to V_{ub} are parametrically suppressed compared to the contributions in the B→J/ψK^{0} time-dependent CP asymmetry alone. This relation uses only SU(3) flavor symmetry, and does not require further diagrammatic assumptions. The current data either fluctuate at the 2σ level from expectations, or may hint at effects of unexpected magnitude from contributions proportional to V_{ub} or from isospin breaking.