Inelastic Rescattering and CP Asymmetries in D -> pi+ pi-, pi0 pi0

We study the direct CP violation induced by inelastic final state interaction (FSI) rescattering in $D\to \pi \pi$ modes, and find that the resultant CP asymmetry is about ${10}^{-4}$ which is larger than ${ϵ}^{\mathrm{\prime }}$ in the K-system. Our estimation is based on well-established theories and experiment measured data, so there are almost no free parameters except the weak phase ${\delta }_{13}$ in the CKM matrix.