Strong and weak phases from time-dependent measurements ofB→ππ

Time dependence in $B^0\mathrm{}\left(t\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}$ and $B^0\mathrm{}\left(t\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}$ is utilized to obtain a maximal set of information on strong and weak phases. One can thereby check theoretical predictions of a small strong phase $\delta$ between penguin and tree amplitudes. A discrete ambiguity between $\delta \simeq 0$ and $\delta \simeq \pi$ may be resolved by comparing the observed charge-averaged branching ratio predicted for the tree amplitude alone, using measurements of $\overrightarrow{B}\pi l\nu$ and factorization, or by direct comparison of Cabibbo-Kobayashi-Maskawa matrix parameters with those determined by other means. It is found that with $150\hspace{0.5em}{\mathrm{fb}}^{-1}$ from BaBar and Belle, this ambiguity will be resolvable if no direct $\mathrm{CP}$ violation is found. In the presence of direct $\mathrm{CP}$ violation, the discrete ambiguity between $\delta$ and $\pi -\delta$ becomes less important, vanishing altogether as $|\delta \overrightarrow{|}\pi /2.\mathrm{}$ The role of measurements involving the lifetime difference between neutral B eigenstates is mentioned briefly.