Strong phases in the decays $B$ to $\pi \pi$

Two sources of strong phases in the decays $B$ to $\pi \pi$ are identified: (1) “quasielastic scattering” corresponding to intermediate states like $\pi \pi$ and $\rho \rho$, (2) “$c\overline{c}$” corresponding to intermediate states like $D\overline{D}$ and $D^{*}{\overline{D}}^{*}$. Possibilities of using data to identify these two sources are discussed and illustrated. Present data suggest both sources may be significant.

Figure 1

The two solutions for the strong phase difference ${\delta }_{20}$ as a function of the ${\pi }^0{\pi }^0$ branching ratio using central values for the other observables and two values of $\gamma$ (solid line $\gamma =67°$, dashed line $\gamma =47°$).