$D \to \pi\pi$ decays with Final State Interactions

We study $D \to \pi\pi$ decays with final state interactions considered in one-particle-exchange method. A clear physical picture for final state interactions based on quark and hadronic level diagrams is presented. A strong phase is introduced for hadronic effective couplings, which is crucial for explaining the experimental data of $D^+\to \pi^+\pi^0$, $D^0\to \pi^+\pi^-$, and $D^0\to \pi^0\pi^0$. Rescattering effects between different $D$ decay channels are usually large. They are important for obtaining correct branching ratios for $D\to \pi\pi$ decays in theoretical calculation.